On the Gaussıan and Mean Curvatures of Parallel Hypersurfaces in E₁ⁿ⁺¹
Ayşe Yaşar Yavuz *
Necmettin Erbakan University, Education of Mathematics, Konya, Turkey.
F. Nejat Ekmekci
Ankara University, Faculty of Sciences, Department of Mathematics, Ankara, Turkey.
Yusuf Yaylı
Ankara University, Faculty of Sciences, Department of Mathematics, Ankara, Turkey.
*Author to whom correspondence should be addressed.
Abstract
Let M be a hypersurfaces in (n+1) dimensional Lorentzian space E₁ⁿ⁺¹ and be a parallel hypersurfaces to M. Before now in [2] the theorem was proved on M in Euclidean space, but now we prove this theorem on in Lorentzian Space. In this study, we give higher order Gaussian curvatures of M in Lorentzian space by using its principal curvatures and we proved the theorem with induction method by using higher order Gaussian curvatures of M in Lorentzian space.
Keywords: Gaussian curvatures, mean curvatures, parallel hypersurfaces, higher order Gaussian curvatures.