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25 results on '"Ergüt, Mahmut"'

5. The Hasimoto Surface According to Bishop Frame

Author

KELLECİ, Alev, BEKTAŞ, Mehmet, and ERGÜT, Mahmut

Subjects
Balıkçılık, Taşınım, Viroloji, Akustik, Deniz ve Tatlı Su Biyolojisi, Mathematics::Analysis of PDEs, Ekoloji, Astronomi ve Astrofizik, Fizik, Kimya, Kuş Bilimi, Hasimoto surface,Smoke ring equation,Bishop frame, Mikroskopi, Uygulamalı, İstatistik ve Olasılık, Tıbbi, İnorganik ve Nükleer, Partiküller ve Alanlar, Limnoloji, Matematik, Mineraloji, Basic Sciences, Temel Bilimler, Oşinografi, Paleontoloji, Spektroskopi, Fizikokimya, Entomoloji, Zooloji, Nükleer, Organik, Parazitoloji, Biyoloji Çeşitliliğinin Korunması, Optik, Akışkanlar ve Plazma, Çevre Bilimleri, Genetik ve Kalıtım, Mantar Bilimi, Termodinamik, Su Kaynakları, Hasimoto yüzeyler,Duman halkası denklemi,Bishop çatısı, Analitik, Atomik ve Moleküler Kimya, Biyoloji, Katı Hal
Abstract

Bu çalışmada Öklidyen 3-uzayındaki Hasimoto yüzeyleriincelenmiştir. İlk olarak, Öklidyen 3-uzayındaki Hasimoto yüzeyleriningeometrik özellikleri incelenmiştir. Özellikle Bishop çatısı ile ilişkilendirilmişbu yüzeylerin eğrilikleri elde edilmiştir. Daha sonrasında bu yüzeylerin Bishopçatısına göre parametre eğrilerinin bazı karakterizasyonları verilmiştir., In this paper, weinvestigate the Hasimoto surfaces in Euclidean 3- space. Firstly, weinvestigate the geometric properties of these surfaces in Euclidean 3-space.Especially, we obtain the curvatures of Hasimoto surface according to Bishopframe. Then we give some characterization of parameter curves obtainedaccording to Bishop frame of Hasimoto surfaces.

Published
2019

7. Motions of Curves in 4-Dimensional Galilean Space G4.

Author

Gün Bozok, Hülya, Aykurt Sepet, Sezin, and Ergüt, Mahmut

Subjects
VECTOR fields, BURGERS' equation, CURVATURE
Abstract

In this paper, we investigate the flow of curve and its equiform geometry in 4-dimensional Galilean space. We obtain that the Frenet equations and curvatures of inextensible flows of curves and its equiformly invariant vector fields and intrinsic quantities are independent of time. We find that the motions of curves and its equiform geometry can be defined by the inviscid and stochastic Burgers' equations in 4-dimensional Galilean space. [ABSTRACT FROM AUTHOR]

Published
2021
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8. Helicoidal Surfaces Which Have the Timelike Axis in Minkowski Space with Density

Author

Yıldız, Önder Gökmen, ERGÜT, Mahmut, and AKYİĞİT, Mahmut

Subjects
Quantitative Biology::Biomolecules, Engineering, Minkowski space,Helicoidal,Manifold with density,Weighted curvature, Mühendislik, Mathematics::Differential Geometry
Abstract

In this paper, we study the prescribed curvature problem in manifold with density. We consider the Minkowski 3-space with a positive density function. For a given plane curve and an axis in the plane in Minkowski 3-space, a helicoidal surface can be constructed by the plane curve under helicoidal motions around the axis. Also we give examples of helicoidal surface with weighted Gaussian curvature.

Published
2018

11. Affine translation surfaces in the isotropic 3-space

Author

AYDİN, Muhittin Evren and ERGÜT, Mahmut

Subjects
Mathematics - Differential Geometry, Differential Geometry (math.DG), FOS: Mathematics, Mathematics::Differential Geometry, 53A35, 53A40, 53B25, Isotropic space,affine translation surface,Weingarten surface
Abstract

The isotropic 3-space \mathbb{I}^{3} is a real affine 3-space endowed with the metric dx^{2}+dy^{2}. In this paper we describe Weingarten and linear Weingarten affine translation surfaces in \mathbb{I}^{3}. Further we classify the affine translation surfaces in \mathbb{I}^{3} that satisfy certain equations in terms of the position vector and the Laplace operator., 11 pages, 3 figures. All comments are welcome

Published
2016

13. MINIMAL AFFINE TRANSLATION SURFACES IN HYPERBOLIC SPACE.

Author

Bozok, Hülya Gün and Ergüt, Mahmut

Subjects
HYPERBOLIC spaces, AFFINE geometry, SURFACE geometry
Abstract

In this paper we study the minimal polynomial affine translation surfaces in the 3-dimensional hyperbolic space H³. We suppose that the affine translation surface is minimal in E3 and then we prove that there are not any minimal polynomial affine translation surfaces in H³. [ABSTRACT FROM AUTHOR]

Published
2018

14. Spacelike biharmonic general helices with timelike normal in the lorentzian group of rigid motions E(2)

Author

Körpinar, Talat, Ergüt, Mahmut, and Turhan, Essin

Subjects
Revistas, Rigid motions, Matemáticas, Biharmonic curve, Harmonic curve, Facultad de Ciencias, Departamento de Matemática
Abstract

In this paper, we study spacelike biharmonic general helices in the Lorentzian group of rigid motions E(2). We characterize the spacelike biharmonic general helices in terms of their curvature and torsion in the Lorentzian group of rigid motions E(2). 92-100 talatkorpinar@gmail.com essin.turhan@gmail.com

Published
2011

17. NEW APPROACH FOR MANNHEIM CURVES IN TERMS OF INEXTENSIBLE FLOWS IN E³.

Author

KÖRPINAR, TALAT and ERGÜT, MAHMUT

Subjects
*PARTIAL differential equations, *SHIPBUILDING, *HARBOR design & construction, *TORSION, *CURVATURE, *MATHEMATICAL models
Abstract

In this work, we study the properties of the Mannheim curves in terms of inextensible flows in E². Using the Frenet frame of the given curve, we present partial differential equations. We give some characterizations for curvatures of a curve in E². [ABSTRACT FROM AUTHOR]

Published
2017

18. Pointwise slant submersions from cosymplectic manifolds.

Author

AYKURT SEPET, Sezin and ERGÜT, Mahmut

Subjects
*SUBMERSIONS (Mathematics), *RIEMANNIAN manifolds, *DIFFERENTIAL geometry, *MANIFOLDS (Mathematics), *RIEMANNIAN submersions
Abstract

In this paper, we characterize the pointwise slant submersions from cosymplectic manifolds onto Riemannian manifolds and give several examples [ABSTRACT FROM AUTHOR]

Published
2016
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20. The equiform differential geometry of curves in 4-dimensional galilean space G4.

Author

Aydin, M. Evren and Ergüt, Mahmut

Subjects
DIFFERENTIAL geometry, HELICES (Algebraic topology), GALILEAN transformation, COORDINATES, CURVES, MATHEMATICAL functions
Abstract

In this paper, we establish equiform differential geometry of curves in 4- dimensional Galilean space G4 . We obtain the angle between the equiform Frenet vectors and their derivatives in G4 . Also, we characterize generalized helices with respect to their equiform curvatures [ABSTRACT FROM AUTHOR]

Published
2013

21. SOME PROPERTIES OF MANNHEIM CURVES IN GALILEAN AND PSEUDO-GALILEAN SPACES.

Author

Öğrenmiş, Alper Osman, Öztekin, Handan, and Ergüt, Mahmut

Subjects
GALILEAN group, TRANSFORMATION groups, CURVES, CURVATURE, CURVES on surfaces
Abstract

The aim of this work is to study the Mannheim curves in 3-dimensional Galilean and pseudo-Galilean space. We obtain the characterizations between the curvatures and torsions of the Mannheim partner curves. [ABSTRACT FROM AUTHOR]

Published
2012

23. Euler-Savary's Formula for the Planar Curves in Two Dimensional Lightlike Cone.

Author

Balgetır Öztekın, Handan and Ergüt, Mahmut

Subjects
*LINEAR operators, *EULER angles, *GRAPHIC methods, *GRAPH theory, *DIFFERENTIAL invariants, *NUMERICAL analysis, *SPACETIME, *WORLD line (Physics)
Abstract

In this paper, we study the Euler-Savary's formula for the planar curves in the lightlike cone. We first define the associated curve of a curve in the two dimensional lightlike cone Q2:Then we give the relation between the curvatures of a base curve, a rolling curve and a roulette which lie on two dimensional lightlike cone Q2. [ABSTRACT FROM AUTHOR]

Published
2010

24. On the ruled surfaces in Minkowski 3-space R1 3.

Author

Öǧrenmiş, Alper, Balgetir, Handan, and Ergüt, Mahmut

Abstract

Izumiya and Takeuchi (2003) obtained some characterizations for Ruled surfaces. Turgut and Hacisalihoğlu (1998) defined timelike Ruled surfaces and obtained some characterizations in timelike Ruled surfaces. Choi (1995) and Jung and Pak (1996) studied Ruled surfaces. This study uses the method in (Izumiya and Takeuchi, 2003) to investigate cylindrical helices and Bertrand curves as curves on timelike Ruled surfaces in Minkowski 3-space R1 3. We have studied singularities of the rectifying developable (surface) of a timelike curve. We observed that the rectifying developable along a timelike curve α is non-singular if and only if α is a cylindrical helice. In this case the rectifying developable is a cylindrical surface. [ABSTRACT FROM AUTHOR]

Published
2006
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25. AN INTEGRAL FORMULA IN QUATERNION SPACE FORM.

Author

Külahci, Mihriban, Bektaş, Mehmet, and Ergüt, Mahmut

Subjects
*QUATERNION functions, *COMPLEX variables, *UNIVERSAL algebra, *COMPLEX numbers, *VECTOR analysis
Abstract

In this paper, we obtained an integral formula in quaternion space form. [ABSTRACT FROM AUTHOR]

Published
2009

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