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Constant Curvatures of Parallel Hypersurfaces in E1n+1Lorentz Space

Received: 26 November 2014     Accepted: 4 December 2014     Published: 12 January 2015
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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.

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), 2015. Published by Science Publishing Group

Keywords

Gaussian Curvatures, Mean Curvatures, Parallel Hypersurface, Higher Order Gaussian Curvatures

References
[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.
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  • 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

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    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

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    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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  • @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}
    }
    

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    T1  - Constant Curvatures of Parallel Hypersurfaces in E1n+1Lorentz Space
    AU  - Ayşe Yavuz
    AU  - F. Nejat Ekmekci
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    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
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    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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Author Information
  • Ankara University, Faculty of Sciences, Department of Mathematics,Ankara, Turkey

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