Constant Curvatures of Parallel Hypersurfaces in E1n+1Lorentz Space
Pure and Applied Mathematics Journal
Volume 4, Issue 1-2, January 2015, Pages: 24-27
Received: Nov. 26, 2014;
Accepted: Dec. 4, 2014;
Published: Jan. 12, 2015
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Ayşe Yavuz, NecmettinErbakan University, Faculty of Education, Education of Mathematics, Konya, Turkey
F. Nejat Ekmekci, Ankara University, Faculty of Sciences, Department of Mathematics,Ankara, Turkey
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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.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.
Gaussian Curvatures, Mean Curvatures, Parallel Hypersurface, Higher Order Gaussian Curvatures
To cite this article
F. Nejat Ekmekci,
Constant Curvatures of Parallel Hypersurfaces in E1n+1Lorentz Space, Pure and Applied Mathematics Journal. Special Issue: Applications of Geometry.
Vol. 4, No. 1-2,
2015, pp. 24-27.
O’Neill, B.,Semi-Riemannian Geometry. Academic PressNew York.1983.
Sağel, M.K. and Hacısalihoğlu, H.H.On the Parallel HypersurfaceWith Constant Curvatures. Commun. Fac. Sci.Univ. Ankara, Ser. A. 1991; 40: 1-5.
Yaşar, A. Higher Order Gaussian Curvatures of a Parallel Hypersurfaces in L_1^n Lorentz Space, Master Thesis. Ankara University; 2010.
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.
Weinstein, T.An Introduction to Lorentz Spaces. Walter De Gruyter. Berlin. New York 1996.