In this paper generalized Gaussian and mean curvatures of a parallel hypersurface in E^(n+1) Euclidean space will be denoted respectively by K ̅ and H ̅, and Generalized Gaussian and mean curvatures of a parallel hypersurface in E₁ⁿ⁺¹ Lorentz space will be denoted respectively by K ̿ and H ̿.Generalized Gaussian curvature and mean curvatures, K ̅and H ̅ofaparallel hypersurface in E^(n+1)Euclidean space are givenin[2].Before nowwe studied relations between curvatures of a hypersurface in Lorentzian space and we introduced higher order Gaussian curvatures of hypersurfaces in Lorentzian space. In this paper, by considering our last studieson higher order Gaussian and mean curvatures, we calculate the generalized K ̿and H ̿ofaparallel hypersurface in E₁ⁿ⁺¹ Lorentz space and we prove theorems about generalized K ̿and H ̿ ofa parallel hypersurface in E₁ⁿ⁺¹ Lorentz space.
| Published in |
Pure and Applied Mathematics Journal (Volume 4, Issue 1-2)
This article belongs to the Special Issue Applications of Geometry |
| DOI | 10.11648/j.pamj.s.2015040102.16 |
| Page(s) | 24-27 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Gaussian Curvatures, Mean Curvatures, Parallel Hypersurface, Higher Order Gaussian Curvatures
| [1] | O’Neill, B.,Semi-Riemannian Geometry. Academic PressNew York.1983. |
| [2] | Sağel, M.K. and Hacısalihoğlu, H.H.On the Parallel HypersurfaceWith Constant Curvatures. Commun. Fac. Sci.Univ. Ankara, Ser. A. 1991; 40: 1-5. |
| [3] | Yaşar, A. Higher Order Gaussian Curvatures of a Parallel Hypersurfaces in L_1^n Lorentz Space, Master Thesis. Ankara University; 2010. |
| [4] | Yavuz, A.,Ekmekci,F. N. and Yaylı Y, On The Gaussian and Mean Curvatures of Parallel Hypersurfaces in E_1^(n+1). British Journal of Mathematics& Computer Sciences. 2014;4(5): 590-596. |
| [5] | Weinstein, T.An Introduction to Lorentz Spaces. Walter De Gruyter. Berlin. New York 1996. |
APA Style
Ayşe Yavuz, F. Nejat Ekmekci. (2015). Constant Curvatures of Parallel Hypersurfaces in E1n+1Lorentz Space. Pure and Applied Mathematics Journal, 4(1-2), 24-27. https://doi.org/10.11648/j.pamj.s.2015040102.16
ACS Style
Ayşe Yavuz; F. Nejat Ekmekci. Constant Curvatures of Parallel Hypersurfaces in E1n+1Lorentz Space. Pure Appl. Math. J. 2015, 4(1-2), 24-27. doi: 10.11648/j.pamj.s.2015040102.16
AMA Style
Ayşe Yavuz, F. Nejat Ekmekci. Constant Curvatures of Parallel Hypersurfaces in E1n+1Lorentz Space. Pure Appl Math J. 2015;4(1-2):24-27. doi: 10.11648/j.pamj.s.2015040102.16
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Download@article{10.11648/j.pamj.s.2015040102.16,
author = {Ayşe Yavuz and F. Nejat Ekmekci},
title = {Constant Curvatures of Parallel Hypersurfaces in E1n+1Lorentz Space},
journal = {Pure and Applied Mathematics Journal},
volume = {4},
number = {1-2},
pages = {24-27},
doi = {10.11648/j.pamj.s.2015040102.16},
url = {https://doi.org/10.11648/j.pamj.s.2015040102.16},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040102.16},
abstract = {In this paper generalized Gaussian and mean curvatures of a parallel hypersurface in E^(n+1) Euclidean space will be denoted respectively by K ̅ and H ̅, and Generalized Gaussian and mean curvatures of a parallel hypersurface in E₁ⁿ⁺¹ Lorentz space will be denoted respectively by K ̿ and H ̿.Generalized Gaussian curvature and mean curvatures, K ̅and H ̅ofaparallel hypersurface in E^(n+1)Euclidean space are givenin[2].Before nowwe studied relations between curvatures of a hypersurface in Lorentzian space and we introduced higher order Gaussian curvatures of hypersurfaces in Lorentzian space. In this paper, by considering our last studieson higher order Gaussian and mean curvatures, we calculate the generalized K ̿and H ̿ofaparallel hypersurface in E₁ⁿ⁺¹ Lorentz space and we prove theorems about generalized K ̿and H ̿ ofa parallel hypersurface in E₁ⁿ⁺¹ Lorentz space.},
year = {2015}
}
TY - JOUR T1 - Constant Curvatures of Parallel Hypersurfaces in E1n+1Lorentz Space AU - Ayşe Yavuz AU - F. Nejat Ekmekci Y1 - 2015/01/12 PY - 2015 N1 - https://doi.org/10.11648/j.pamj.s.2015040102.16 DO - 10.11648/j.pamj.s.2015040102.16 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 24 EP - 27 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.s.2015040102.16 AB - In this paper generalized Gaussian and mean curvatures of a parallel hypersurface in E^(n+1) Euclidean space will be denoted respectively by K ̅ and H ̅, and Generalized Gaussian and mean curvatures of a parallel hypersurface in E₁ⁿ⁺¹ Lorentz space will be denoted respectively by K ̿ and H ̿.Generalized Gaussian curvature and mean curvatures, K ̅and H ̅ofaparallel hypersurface in E^(n+1)Euclidean space are givenin[2].Before nowwe studied relations between curvatures of a hypersurface in Lorentzian space and we introduced higher order Gaussian curvatures of hypersurfaces in Lorentzian space. In this paper, by considering our last studieson higher order Gaussian and mean curvatures, we calculate the generalized K ̿and H ̿ofaparallel hypersurface in E₁ⁿ⁺¹ Lorentz space and we prove theorems about generalized K ̿and H ̿ ofa parallel hypersurface in E₁ⁿ⁺¹ Lorentz space. VL - 4 IS - 1-2 ER -
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