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Your search keyword '"Orthonormal frame"' showing total 280 results
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280 results on '"Orthonormal frame"'

1. Some aspects of normal curve on smooth surface under isometry

Author

Singh Kuljeet, Sharma Sandeep, and Bhardwaj Arun Kumar

Subjects
normal curves, isometry, geodesic, normal curvature, orthonormal frame, 53a04, 53a05, 53a15, 51m05, Mathematics, QA1-939
Abstract

The normal curve is a space curve that plays an important role in the field of differential geometry. This research focuses on analyzing the properties of normal curves on smooth immersed surfaces, considering their invariance under isometric transformations. The primary contribution of this article is to explore the requirements for the image of a normal curve that preserves its invariance under isometric transformations. In this article, we investigate the invariant condition for the component of the position vector of the normal curves under isometry and compute the expression for the normal and geodesic curvature of such curves. Moreover, it has been investigated that the geodesic curvature and Christoffel symbols remain unchanged under the isometry of surfaces in R3{{\mathbb{R}}}^{3}.

Published
2024
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2. On the geometry of tangent bundle of a hypersurface in ℝn+1.

Author

YURTTANÇIKMAZ, Semra

Subjects
*TANGENT bundles, *TANGENTS (Geometry), *CURVATURE
Abstract

In this paper, tangent bundle TM of the hypersurface M in ℝn+1 has been studied. For hypersurface M given by immersion f : M → ℝn+1, considering the fact that F = df : TM → R2n+2 is also immersion, TM is treated as a submanifold of ℝ2n+2. Firstly, an induced metric which is called rescaled induced metric has been defined on TM, and the Levi-Civita connection has been calculated for this metric. Next, curvature tensors of tangent bundle TM have been obtained. Finally, the orthonormal frame at the point (p, u) ∈ TM has been defined and some curvature properties of such a tangent bundle by means of orthonormal frame for a given point have been investigated. [ABSTRACT FROM AUTHOR]

Published
2021
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3. On the geometry of tangent bundle of a hypersurface in ℝn+1.

Author

YURTTANÇIKMAZ, Semra

Subjects
TANGENT bundles, TANGENTS (Geometry), CURVATURE
Abstract

In this paper, tangent bundle TM of the hypersurface M in ℝn+1 has been studied. For hypersurface M given by immersion f : M → ℝn+1, considering the fact that F = df : TM → R2n+2 is also immersion, TM is treated as a submanifold of ℝ2n+2. Firstly, an induced metric which is called rescaled induced metric has been defined on TM, and the Levi-Civita connection has been calculated for this metric. Next, curvature tensors of tangent bundle TM have been obtained. Finally, the orthonormal frame at the point (p, u) ∈ TM has been defined and some curvature properties of such a tangent bundle by means of orthonormal frame for a given point have been investigated. [ABSTRACT FROM AUTHOR]

Published
2021
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4. Piecewise Conserved Quantities

Author

Dray, Tevian, van Beijeren, Henk, Series editor, Blanchard, Philippe, Series editor, Busch, Paul, Series editor, Coecke, Bob, Series editor, Dieks, Dennis, Series editor, Dittrich, Bianca, Series editor, Dürr, Detlef, Series editor, Durrer, Ruth, Series editor, Frigg, Roman, Series editor, Fuchs, Christopher, Series editor, Ghirardi, Giancarlo, Series editor, Giulini, Domenico J. W., Series editor, Jaeger, Gregg, Series editor, Kiefer, Claus, Series editor, Landsman, Nicolaas P., Series editor, Maes, Christian, Series editor, Murao, Mio, Series editor, Nicolai, Hermann, Series editor, Petkov, Vesselin, Series editor, Ruetsche, Laura, Series editor, Sakellariadou, Mairi, Series editor, van der Merwe, Alwyn, Series editor, Verch, Rainer, Series editor, Werner, Reinhard F., Series editor, Wüthrich, Christian, Series editor, Young, Lai-Sang, Series editor, Bagla, Jasjeet Singh, editor, and Engineer, Sunu, editor

Published
2017
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14. Surface Topology and Geometry

Author

Zeng, Wei, Gu, Xianfeng David, Alladi, Krishnaswami, Series editor, Bellomo, Nicola, Series editor, Benzi, Michele, Series editor, Li, Tatsien, Series editor, Neufang, Matthias, Series editor, Scherzer, Otmar, Series editor, Schleicher, Dierk, Series editor, Sidoravicius, Vladas, Series editor, Steinberg, Benjamin, Series editor, Tschinkel, Yuri, Series editor, Tu, Loring W., Series editor, Zhang, Ping, Series editor, Zeng, Wei, and Gu, Xianfeng David

Published
2013
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21. On Orthogonal Strassen Tensor Decomposition.

Author

Luo, Ming, Zhang, Yichao, Dong, Hailing, Yang, Ming, and Liu, Wen

Subjects
ORTHOGONAL systems, CALCULUS of tensors, ALGORITHMS, DECOMPOSITION method, PROBLEM solving
Abstract

In this paper, we introduce tensor decomposition with orthonormal frame. With the help of ADMM joint diagonal algorithm, we propose a CP tensor decomposition in orthonormal frame, named Orthogonal Strassen Tensor Decomposition. [ABSTRACT FROM AUTHOR]

Published
2018
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40. The Einstein-Hilbert Action as a Spectral Action

Author

Ammann, Bernd, Bär, Christian, Beig, R., editor, Englert, B. -G., editor, Frisch, U., editor, Hänggi, P., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, v. Löhneysen, H., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, Scheck, Florian, editor, Upmeier, Harald, editor, and Werner, Wend, editor

Published
2002
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41. Exact Discretization of Harmonic Tensors

Author

Timothy Chumley, Renato Feres, and Matthew Wallace

Subjects
Mathematics - Differential Geometry, Discretization, 010102 general mathematics, Connection (vector bundle), Mathematical analysis, Holonomy, Harmonic (mathematics), Orthonormal frame, 01 natural sciences, Potential theory, Tensor field, 010104 statistics & probability, Differential Geometry (math.DG), Harmonic function, FOS: Mathematics, 0101 mathematics, Analysis, Mathematics
Abstract

Lyons and Sullivan have shown how to discretize harmonic functions on a Riemannian manifold $M$ whose Brownian motion satisfies a certain recurrence property called $\ast$-recurrence. We study analogues of this discretization for tensor fields which are harmonic in the sense of the covariant Laplacian. We show that, under certain restrictions on the holonomy of the connection, the lifted diffusion on the orthonormal frame bundle has the same $\ast$-recurrence property as the original Brownian motion. This observation permits us to reduce to the discretization of ordinary harmonic functions by a device called scalarization., Comment: 15 pages

Published
2021
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48. A stable finite element method for low inertia undulatory locomotion in three dimensions

Author

Ranner, T

Subjects
Numerical Analysis, Applied Mathematics, media_common.quotation_subject, Numerical analysis, Mathematical analysis, Numerical Analysis (math.NA), 010103 numerical & computational mathematics, Orthonormal frame, Inertia, 01 natural sciences, Finite element method, 010101 applied mathematics, Piecewise linear function, Computational Mathematics, Undulatory locomotion, FOS: Mathematics, Piecewise, Mathematics - Numerical Analysis, 0101 mathematics, Orthonormality, media_common, Mathematics
Abstract

We present and analyse a numerical method for understanding the low-inertia dynamics of an open, inextensible viscoelastic rod - a long and thin three dimensional object - representing the body of a long, thin microswimmer. Our model allows for both elastic and viscous, bending and twisting deformations and describes the evolution of the midline curve of the rod as well as an orthonormal frame which fully determines the rod's three dimensional geometry. The numerical method is based on using a combination of piecewise linear and piecewise constant finite element functions based on a novel rewriting of the model equations. We derive a stability estimate for the semi-discrete scheme and show that at the fully discrete level that we have good control over the length element and preserve the frame orthonormality conditions up to machine precision. Numerical experiments demonstrate both the good properties of the method as well as the applicability of the method for simulating undulatory locomotion in the low-inertia regime.

Published
2020
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49. Recovering the Normal Form and Symmetry Class of an Elasticity Tensor

Author

Sophie Abramian, Marc Olive, Boris Desmorat, Rodrigue Desmorat, and Boris Kolev

Subjects
Pure mathematics, Class (set theory), Mechanical Engineering, 02 engineering and technology, Orthonormal frame, Characterization (mathematics), 01 natural sciences, 010101 applied mathematics, 020303 mechanical engineering & transports, 0203 mechanical engineering, Mechanics of Materials, General Materials Science, Tensor, 0101 mathematics, Symmetry (geometry), Elasticity tensor, Anisotropy, Rotation (mathematics), Mathematics
Abstract

We propose an effective geometrical approach to recover the normal form of a given Elasticity tensor. We produce a rotation which brings an Elasticity tensor onto its normal form, given its components in any orthonormal frame, and this for any tensor of any symmetry class. Our methodology relies on the use of specific covariants and on the geometric characterization of each symmetry class using these covariants. An algorithm to detect the symmetry class of an Elasticity tensor is finally formulated.

Published
2020
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