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52. Movement disorder society criteria for clinically established early Parkinson's disease

Author

Berg, Daniela, Adler, Charles H, Bloem, Bastiaan R, Chan, Piu, Gasser, Thomas, Goetz, Christopher G, Halliday, Glenda, Lang, Anthony E, Lewis, Simon, Li, Yuan, Liepelt‐Scarfone, Inga, Litvan, Irene, Marek, Kenneth, Maetzler, Corina, Mi, Taomian, Obeso, José, Oertel, Wolfgang, Olanow, C Warren, Poewe, Werner, Rios‐Romenets, Silvia, Schäffer, Eva, Seppi, Klaus, Heim, Beatrice, Slow, Elizabeth, Stern, Matthew, Bledsoe, Ian O, Deuschl, Günther, and Postuma, Ronald B

Subjects
Neurodegenerative, Neurosciences, Brain Disorders, Aging, Prevention, Parkinson's Disease, 4.1 Discovery and preclinical testing of markers and technologies, 4.2 Evaluation of markers and technologies, Detection, screening and diagnosis, Neurological, Aged, Female, Humans, International Cooperation, Male, Middle Aged, Parkinson Disease, Reproducibility of Results, Sensitivity and Specificity, Severity of Illness Index, Societies, Medical, Parkinson's disease, diagnosis, criteria, Clinical Sciences, Human Movement and Sports Sciences, Neurology & Neurosurgery
Abstract

BackgroundIn 2015, the International Parkinson and Movement Disorder Society published clinical diagnostic criteria for Parkinson's disease (PD). Although recent validation studies suggest high accuracy, one unmet need is for highly specific criteria for clinical trials in early/de novo PD.ObjectivesThe objective of this study was to generate and test a PD diagnostic criteria termed "clinically established early PD."MethodsWe modified the Movement Disorder Society criteria to increase specificity for early PD by removing all disease duration components and changing red flags to absolute exclusions. We then estimated the sensitivity/specificity of clinically established early PD criteria in patients with disease duration

Published
2018

55. Deficiency in endocannabinoid synthase DAGLB contributes to early onset Parkinsonism and murine nigral dopaminergic neuron dysfunction

Author

Liu, Zhenhua, Yang, Nannan, Dong, Jie, Tian, Wotu, Chang, Lisa, Ma, Jinghong, Guo, Jifeng, Tan, Jieqiong, Dong, Ao, He, Kaikai, Zhou, Jingheng, Cinar, Resat, Wu, Junbing, Salinas, Armando G., Sun, Lixin, Kumar, Mantosh, Sullivan, Breanna T., Oldham, Braden B., Pitz, Vanessa, Makarious, Mary B., Ding, Jinhui, Kung, Justin, Xie, Chengsong, Hawes, Sarah L., Wang, Lupeng, Wang, Tao, Chan, Piu, Zhang, Zhuohua, Le, Weidong, Chen, Shengdi, Lovinger, David M., Blauwendraat, Cornelis, Singleton, Andrew B., Cui, Guohong, Li, Yulong, Cai, Huaibin, and Tang, Beisha

Published
2022
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59. High-density lipoprotein subclasses and cardiovascular disease and mortality in type 2 diabetes: analysis from the Hong Kong Diabetes Biobank

Author

Jin, Qiao, Lau, Eric S. H., Luk, Andrea O., Tam, Claudia H. T., Ozaki, Risa, Lim, Cadmon K. P., Wu, Hongjiang, Chow, Elaine Y. K., Kong, Alice P. S., Lee, Heung Man, Fan, Baoqi, Ng, Alex C. W., Jiang, Guozhi, Lee, Ka Fai, Siu, Shing Chung, Hui, Grace, Tsang, Chiu Chi, Lau, Kam Piu, Leung, Jenny Y., Tsang, Man-wo, Cheung, Elaine Y. N., Kam, Grace, Lau, Ip Tim, Li, June K., Yeung, Vincent T., Lau, Emmy, Lo, Stanley, Fung, Samuel, Cheng, Yuk Lun, Chow, Chun Chung, Yu, Weichuan, Tsui, Stephen K. W., Huang, Yu, Lan, Hui-yao, Szeto, Cheuk Chun, So, Wing Yee, Jenkins, Alicia J., Chan, Juliana C. N., and Ma, Ronald C. W.

Published
2022
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60. Using a Simulation Game to Make Learning about Angles Meaningful. An Exploratory Study in Primary School

Author

Piu, Angela, Fregola, Cesare, and Santoro, Anna

Abstract

As indicated in numerous research studies, schoolchildren encounter many difficulties and obstacles in learning the multifaceted concept of the angle. In order to explore the possibility of enhancing schoolchildren's understanding of such a concept, the authors present a study that aims at investigating some structural characteristics of Angolandia, a simulation game for learning about angles specifically designed according to theoretical-methodological choices for which references were initially drawn from the literature on simulation games and teaching mathematics. This research, involving 31 children from two, 4th-year primary school classes who played Angolandia, reports the observations made as the game was played, an analysis of a written interview on the angle with children before and after the educational activity and an interview with their teachers. These initial data are discussed and considered as the point of departure for systematic experimentation and future developments.

Published
2016

64. OMSV enables accurate and comprehensive identification of large structural variations from nanochannel-based single-molecule optical maps

Author

Li, Le, Leung, Alden King-Yung, Kwok, Tsz-Piu, Lai, Yvonne YY, Pang, Iris K, Chung, Grace Tin-Yun, Mak, Angel CY, Poon, Annie, Chu, Catherine, Li, Menglu, Wu, Jacob JK, Lam, Ernest T, Cao, Han, Lin, Chin, Sibert, Justin, Yiu, Siu-Ming, Xiao, Ming, Lo, Kwok-Wai, Kwok, Pui-Yan, Chan, Ting-Fung, and Yip, Kevin Y

Subjects
Computational Biology, Computer Simulation, Genome, Human, Genomic Structural Variation, Genomics, Humans, Software, Optical mapping, Nanochannel, Single-molecule analysis, Structural variation, Environmental Sciences, Biological Sciences, Information and Computing Sciences, Bioinformatics
Abstract

We present a new method, OMSV, for accurately and comprehensively identifying structural variations (SVs) from optical maps. OMSV detects both homozygous and heterozygous SVs, SVs of various types and sizes, and SVs with or without creating or destroying restriction sites. We show that OMSV has high sensitivity and specificity, with clear performance gains over the latest method. Applying OMSV to a human cell line, we identified hundreds of SVs >2 kbp, with 68 % of them missed by sequencing-based callers. Independent experimental validation confirmed the high accuracy of these SVs. The OMSV software is available at http://yiplab.cse.cuhk.edu.hk/omsv/ .

Published
2017

65. OMBlast: alignment tool for optical mapping using a seed-and-extend approach

Author

Leung, Alden King-Yung, Kwok, Tsz-Piu, Wan, Raymond, Xiao, Ming, Kwok, Pui-Yan, Yip, Kevin Y, and Chan, Ting-Fung

Subjects
Biological Sciences, Bioinformatics and Computational Biology, Bioengineering, Generic health relevance, Animals, Caenorhabditis elegans, Escherichia coli, Genome, Genomics, Humans, Optical Restriction Mapping, Saccharomyces cerevisiae, Sequence Alignment, Sequence Analysis, DNA, Software, Mathematical Sciences, Information and Computing Sciences, Bioinformatics, Biological sciences, Information and computing sciences, Mathematical sciences
Abstract

BackgroundOptical mapping is a technique for capturing fluorescent signal patterns of long DNA molecules (in the range of 0.1–1 Mbp). Recently, it has been complementing the widely used short-read sequencing technology by assisting with scaffolding and detecting large and complex structural variations (SVs). Here, we introduce a fast, robust and accurate tool called OMBlast for aligning optical maps, the set of signal locations on the molecules generated from optical mapping. Our method is based on the seed-and-extend approach from sequence alignment, with modifications specific to optical mapping.ResultsExperiments with both synthetic and our real data demonstrate that OMBlast has higher accuracy and faster mapping speed than existing alignment methods. Our tool also shows significant improvement when aligning data with SVs.Availability and implementationOMBlast is implemented for Java 1.7 and is released under a GPL license. OMBlast can be downloaded from https://github.com/aldenleung/OMBlast and run directly on machines equipped with a Java virtual machine.Contactkevinyip@cse.cuhk.edu.hk and tf.chan@cuhk.edu.hkSupplementary informationSupplementary data are available at Bioinformatics online.

Published
2017

69. Invariant submanifolds of metric contact pairs

Author

Hadjar, Amine and Piu, Paola

Subjects
Mathematics - Differential Geometry, 53C25 (Primary), 53B20, 53D10, 53B35, 53C12 (Secondary)
Abstract

We show that $\phi$-invariant submanifolds of metric contact pairs with orthogonal characteristic foliations make constant angles with the Reeb vector fields. Our main result is that for the normal case such submanifolds of dimension at least $2$ are all minimal. We prove that an odd-dimensional $\phi$-invariant submanifold of a metric contact pair with orthogonal characteristic foliations inherits a contact form with an almost contact metric structure, and this induced structure is contact metric if and only if the submanifold is tangent to one Reeb vector field and orthogonal to the other one. Furthermore we show that the leaves of the two characteristic foliations of the differentials of the contact pair are minimal. We also prove that when one Reeb vector field is Killing and spans one characteristic foliation, the metric contact pair is a product of a contact metric manifold with $\mathbb{R}$., Comment: 15 pages

Published
2015

74. Single-cell transcriptomic atlas of primate cardiopulmonary aging

Author

Ma, Shuai, Sun, Shuhui, Li, Jiaming, Fan, Yanling, Qu, Jing, Sun, Liang, Wang, Si, Zhang, Yiyuan, Yang, Shanshan, Liu, Zunpeng, Wu, Zeming, Zhang, Sheng, Wang, Qiaoran, Zheng, Aihua, Duo, Shuguang, Yu, Yang, Belmonte, Juan Carlos Izpisua, Chan, Piu, Zhou, Qi, Song, Moshi, Zhang, Weiqi, and Liu, Guang-Hui

Published
2021
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81. Genome-Wide Structural Variation Detection by Genome Mapping on Nanochannel Arrays.

Author

Mak, Angel CY, Lai, Yvonne YY, Lam, Ernest T, Kwok, Tsz-Piu, Leung, Alden KY, Poon, Annie, Mostovoy, Yulia, Hastie, Alex R, Stedman, William, Anantharaman, Thomas, Andrews, Warren, Zhou, Xiang, Pang, Andy WC, Dai, Heng, Chu, Catherine, Lin, Chin, Wu, Jacob JK, Li, Catherine ML, Li, Jing-Woei, Yim, Aldrin KY, Chan, Saki, Sibert, Justin, Džakula, Željko, Cao, Han, Yiu, Siu-Ming, Chan, Ting-Fung, Yip, Kevin Y, Xiao, Ming, and Kwok, Pui-Yan

Subjects
Cell Line, Humans, Microarray Analysis, Chromosome Mapping, Genome, Human, Genomic Structural Variation, biotechnology, genome mapping, structural variation detection, Genome, Human, Developmental Biology, Genetics
Abstract

Comprehensive whole-genome structural variation detection is challenging with current approaches. With diploid cells as DNA source and the presence of numerous repetitive elements, short-read DNA sequencing cannot be used to detect structural variation efficiently. In this report, we show that genome mapping with long, fluorescently labeled DNA molecules imaged on nanochannel arrays can be used for whole-genome structural variation detection without sequencing. While whole-genome haplotyping is not achieved, local phasing (across >150-kb regions) is routine, as molecules from the parental chromosomes are examined separately. In one experiment, we generated genome maps from a trio from the 1000 Genomes Project, compared the maps against that derived from the reference human genome, and identified structural variations that are >5 kb in size. We find that these individuals have many more structural variants than those published, including some with the potential of disrupting gene function or regulation.

Published
2016

82. Pseudo-Riemannian Symmetries on Heisenberg groups

Author

Goze, Michel, Piu, Paola, and Remm, Elisabeth

Subjects
Mathematics - Differential Geometry, 22F30, 53C30, 53C35, 17B70
Abstract

The notion of $\Gamma$-symmetric space is a natural generalization of the classical notion of symmetric space based on $\Z_2$-grading of Lie algebras. In our case, we consider homogeneous spaces $G/H$ such that the Lie algebra $\g$ of $G$ admits a $\Gamma$-grading where $\Gamma$ is a finite abelian group. In this work we study Riemannian metrics and Lorentzian metrics on the Heisenberg group $\mathbb{H}_3$ adapted to the symmetries of a $\Gamma$-symmetric structure on $\mathbb{H}_3$. We prove that the classification of $\z$-symmetric Riemannian and Lorentzian metrics on $\mathbb{H}_3$ corresponds to the classification of left-invariant Riemannian and Lorentzian metrics, up to isometry. We study also the $\Z_2^k$-symmetric structures on $G/H$ when $G$ is the $(2p+1)$-dimensional Heisenberg group for $k \geq 1$. This gives examples of non riemannian symmetric spaces. When $k \geq 1$, we show that there exists a family of flat and torsion free affine connections adapted to the $\Z_2^k$-symmetric structures., Comment: 17 pages. arXiv admin note: text overlap with arXiv:1201.0447

Published
2014

87. MDS clinical diagnostic criteria for Parkinson's disease.

Author

Postuma, Ronald B, Berg, Daniela, Stern, Matthew, Poewe, Werner, Olanow, C Warren, Oertel, Wolfgang, Obeso, José, Marek, Kenneth, Litvan, Irene, Lang, Anthony E, Halliday, Glenda, Goetz, Christopher G, Gasser, Thomas, Dubois, Bruno, Chan, Piu, Bloem, Bastiaan R, Adler, Charles H, and Deuschl, Günther

Subjects
Humans, Parkinson Disease, Severity of Illness Index, Neuropsychological Tests, Reference Standards, Societies, Scientific, Parkinson's disease, absolute exclusion criteria, clinical diagnostic criteria, motor parkinsonism, non-motor manifestations, red flags, supportive criteria, Neurology & Neurosurgery, Clinical Sciences, Human Movement and Sports Sciences, Cognitive Sciences
Abstract

This document presents the Movement Disorder Society Clinical Diagnostic Criteria for Parkinson's disease (PD). The Movement Disorder Society PD Criteria are intended for use in clinical research but also may be used to guide clinical diagnosis. The benchmark for these criteria is expert clinical diagnosis; the criteria aim to systematize the diagnostic process, to make it reproducible across centers and applicable by clinicians with less expertise in PD diagnosis. Although motor abnormalities remain central, increasing recognition has been given to nonmotor manifestations; these are incorporated into both the current criteria and particularly into separate criteria for prodromal PD. Similar to previous criteria, the Movement Disorder Society PD Criteria retain motor parkinsonism as the core feature of the disease, defined as bradykinesia plus rest tremor or rigidity. Explicit instructions for defining these cardinal features are included. After documentation of parkinsonism, determination of PD as the cause of parkinsonism relies on three categories of diagnostic features: absolute exclusion criteria (which rule out PD), red flags (which must be counterbalanced by additional supportive criteria to allow diagnosis of PD), and supportive criteria (positive features that increase confidence of the PD diagnosis). Two levels of certainty are delineated: clinically established PD (maximizing specificity at the expense of reduced sensitivity) and probable PD (which balances sensitivity and specificity). The Movement Disorder Society criteria retain elements proven valuable in previous criteria and omit aspects that are no longer justified, thereby encapsulating diagnosis according to current knowledge. As understanding of PD expands, the Movement Disorder Society criteria will need continuous revision to accommodate these advances.

Published
2015

88. MDS research criteria for prodromal Parkinson's disease.

Author

Berg, Daniela, Postuma, Ronald B, Adler, Charles H, Bloem, Bastiaan R, Chan, Piu, Dubois, Bruno, Gasser, Thomas, Goetz, Christopher G, Halliday, Glenda, Joseph, Lawrence, Lang, Anthony E, Liepelt-Scarfone, Inga, Litvan, Irene, Marek, Kenneth, Obeso, José, Oertel, Wolfgang, Olanow, C Warren, Poewe, Werner, Stern, Matthew, and Deuschl, Günther

Subjects
Humans, Parkinson Disease, Severity of Illness Index, Societies, Scientific, Prodromal Symptoms, Parkinson's disease, diagnosis, prodromal, Neurology & Neurosurgery, Clinical Sciences, Human Movement and Sports Sciences, Cognitive Sciences
Abstract

This article describes research criteria and probability methodology for the diagnosis of prodromal PD. Prodromal disease refers to the stage wherein early symptoms or signs of PD neurodegeneration are present, but classic clinical diagnosis based on fully evolved motor parkinsonism is not yet possible. Given the lack of clear neuroprotective/disease-modifying therapy for prodromal PD, these criteria were developed for research purposes only. The criteria are based upon the likelihood of prodromal disease being present with probable prodromal PD defined as ≥80% certainty. Certainty estimates rely upon calculation of an individual's risk of having prodromal PD, using a Bayesian naïve classifier. In this methodology, a previous probability of prodromal disease is delineated based upon age. Then, the probability of prodromal PD is calculated by adding diagnostic information, expressed as likelihood ratios. This diagnostic information combines estimates of background risk (from environmental risk factors and genetic findings) and results of diagnostic marker testing. In order to be included, diagnostic markers had to have prospective evidence documenting ability to predict clinical PD. They include motor and nonmotor clinical symptoms, clinical signs, and ancillary diagnostic tests. These criteria represent a first step in the formal delineation of early stages of PD and will require constant updating as more information becomes available.

Published
2015

90. A 36-week multicenter, randomized, double-blind, placebo-controlled, parallel-group, phase 3 clinical trial of sodium oligomannate for mild-to-moderate Alzheimer’s dementia

Author

Xiao, Shifu, Chan, Piu, Wang, Tao, Hong, Zhen, Wang, Shuzhen, Kuang, Weihong, He, Jincai, Pan, Xiaoping, Zhou, Yuying, Ji, Yong, Wang, Luning, Cheng, Yan, Peng, Ying, Ye, Qinyong, Wang, Xiaoping, Wu, Yuncheng, Qu, Qiumin, Chen, Shengdi, Li, Shuhua, Chen, Wei, Xu, Jun, Peng, Dantao, Zhao, Zhongxin, Li, Yansheng, Zhang, Junjian, Du, Yifeng, Chen, Weixian, Fan, Dongsheng, Yan, Yong, Liu, Xiaowei, Zhang, Wei, Luo, Benyan, Wu, Wenyuan, Shen, Lu, Liu, Chunfeng, Mao, Peixian, Wang, Qiumei, Zhao, Qianhua, Guo, Qihao, Zhou, Yongtao, Li, Yi, Jiang, Lijun, Ren, Wenwei, Ouyang, Yingjun, Wang, Yan, Liu, Shuai, Jia, Jianjun, Zhang, Nan, Liu, Zhonglin, He, Raoli, Feng, Tingyi, Lu, Wenhui, Tang, Huidong, Gao, Ping, Zhang, Yingchun, Chen, Lanlan, Wang, Lei, Yin, You, Xu, Qun, Xiao, Jinsong, Cong, Lin, Cheng, Xi, Zhang, Hui, Gao, Dan, Xia, Minghua, Lian, Tenghong, Peng, Guoping, Zhang, Xu, Jiao, Bin, Hu, Hua, Chen, Xueyan, Guan, Yihui, Cui, Ruixue, Huang, Qiu, Xin, Xianliang, Chen, Hongjian, Ding, Yu, Zhang, Jing, Feng, Teng, Cantillon, Marc, Chen, Kewei, Cummings, Jeffrey L., Ding, Jian, Geng, Meiyu, and Zhang, Zhenxin

Published
2021
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95. Riemannian symmetries in flag manifolds

Author

Piu, Paola and Remm, Elisabeth

Subjects
Mathematics - Differential Geometry, 53C30
Abstract

Flag manifolds are in general not symmetric spaces. But they are provided with a structure of $\mathbb{Z}_2^k$-symmetric space. We describe the Riemannian metrics adapted to this structure and some properties of reducibility. We detail for the flag manifold $SO(5)/SO(2)\times SO(2) \times SO(1)$ what are the conditions for a metric adapted to the $\mathbb{Z}_2^2$-symmetric structure to be naturally reductive., Comment: 11 pages

Published
2012

96. Surfaces in three-dimensional space forms with divergence-free stress-bienergy tensor

Author

Caddeo, R., Montaldo, S., Oniciuc, C., and Piu, P.

Subjects
Mathematics - Differential Geometry
Abstract

We introduce the notion of biconservative hypersurfaces, that is hypersurfaces with conservative stress-energy tensor with respect to the bienergy. We give the (local) classification of biconservative surfaces in 3-dimensional space forms., Comment: Final version to appear in Ann. Mat. Pura Appl

Published
2012

97. Pseudo-Riemannian Symmetries on Heisenberg group $\mathbb{H}_{3}$

Author

Goze, Michel and Piu, Paola

Subjects
Mathematics - Differential Geometry, 22F30, 53C30, 53C35, 17B70
Abstract

The notion of $\Gamma$-symmetric space is a natural generalization of the classical notion of symmetric space based on $\z_2$-grading of Lie algebras. In our case, we consider homogeneous spaces $G/H$ such that the Lie algebra $\g$ of $G$ admits a $\Gamma$-grading where $\Gamma$ is a finite abelian group. In this work we study Riemannian metrics and Lorentzian metrics on the Heisenberg group $\mathbb{H}_3$ adapted to the symmetries of a $\Gamma$-symmetric structure on $\mathbb{H}_3$. We prove that the classification of $\z_2^2$-symmetric Riemannian and Lorentzian metrics on $\mathbb{H}_3$ corresponds to the classification of left invariant Riemannian and Lorentzian metrics, up to isometries. This gives examples of non-symmetric Lorentzian homogeneous spaces., Comment: 18 pages

Published
2012

98. Data-Driven Subtypes of Multiple System Atrophy and Their Implications for Prognosis

Author

Fan, Cheng-Cheng, Han, Chao, Wang, Xue-Mei, Chhetri, Jagadish K., Mao, Wei, Xu, Er-He, Liu, Shu-Ying, and Chan, Piu

Abstract

Background: While multiple system atrophy (MSA) presents with high heterogeneous motor and nonmotor symptoms, the associations between clinical phenotypes and prognosis are unclear.Objective: We aimed to evaluate clinical phenotypes of MSA using data-driven approach and measure the impact of phenotypes on survival and bedbound status.Methods: 193 MSA patients were recruited from Xuanwu Hospital Capital Medical University, whose history, motor and non-motor symptoms were examined using cluster analysis. Ninety-five participants were followed-up via telephone after a mean of 31.87 months. We employed Kaplan– Meier analysis to examine survival and performed Cox and logistic regression analyses to identify factors associated with survival and bedbound status.Results: We identified four clinical profiles of MSA: cerebellar symptom-dominant, sleep and mood disorder-dominant, rigid akinetic-dominant, and malignant diffuse. The overall median survival was 7.75 years (95% CI 7.19–8.31). After adjusting for years from symptom onset to diagnosis, age and sex, patients in the malignant diffuse and rigid akinetic-dominant clusters had greater risk of death than sleep and mood disorder-dominant cluster. Furthermore, patients in the malignant diffuse and rigid akinetic-dominant clusters had higher risk of being bedbound than cerebellar symptom-dominant cluster.Conclusions: The malignant diffuse and sleep and mood disorder-dominant were identified besides the two classical subtypes, parkinsonism, and cerebellar symptom-variant. Patients with rigid-akinetic motor profiles have a worse prognosis than cerebellar symptom-dominant profiles in general. Diffuse symptoms, especially postural instability, and cognitive alterations at diagnosis, indicate rapid functional loss and disease progression. The different profiles and prognoses might indicate varied underlying pathological mechanisms.

Published
2024
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99. On the three-dimensional homogeneous SO(2) - isotropic Riemannian manifolds

Author

Piu, P. and Profir, M. M.

Subjects
Mathematics - Differential Geometry
Abstract

In this paper we consider some properties of the three-dimensional homogeneous SO(2)-isotropic Riemannian manifolds. In particular, we determine the geodesics, the totally geodesic surfaces, the totally umbilical surfaces and the geodesics of the rotational surfaces., Comment: 14 pages, 5 figures

Published
2010

100. Geodesicity and Isoclinity Properties for the Tangent Bundle of the Heisenberg Manifold with Sasaki Metric

Author

Druta, Simona-Luiza and Piu, Maria Paola

Subjects
Mathematics - Differential Geometry
Abstract

We prove that the horizontal and vertical distributions of the tangent bundle with the Sasaki metric are isocline, the distributions given by the kernels of the horizontal and vertical lifts of the contact form $\omega$ from the Heisenberg manifold $(H_3,g)$ to $(TH_3,g^S)$ are not totally geodesic, and the distributions $F^H=L(E_1^H,E_2^H)$ and $F^V=L(E_1^V,E_2^V)$ are totally geodesic, but they are not isocline. We obtain that the horizontal and natural lifts of the curves from the Heisenberg manifold $(H_3,g)$, are geodesics in the tangent bundle endowed with the Sasaki metric $(TH_3,g^s)$, if and only if the curves considered on the base manifold are geodesics. Then, we get two particular examples of geodesics from $(TH_3,g^s)$, which are not horizontal or natural lifts of geodesics from the base manifold $(H_3,g)$., Comment: 12 pages

Published
2010

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