Science Journal Of Mathematics and Statistics, Volume 2016, April 2016
ISSN:2276-6324
© Author(s) 2016. This work is distributed under the Creative Commons Attribution 3.0 License.
Research Article
On The Generalized Gaussian and Mean curvatures in E1n+1
Author: Ayse Yavuz, F. Nejat Ekmekci
Department of Secondary Science and Mathematics Education, Necmettin Erbakan University, Konya, Turkey Department of Mathematics, Faculty of Sciences, Ankara University, , Ankara, Turkey
Accepted 16 December, 2015; Available Online 12 April 2016
doi: 10.7237/sjms/111
Abstract:
Before now in [2] the generalized Gaussian and mean curvatures were proved in Euclidean space, but now we prove the theorems in Lorentzian Space. In our previous paper, we have studied higher order Gaussian curvatures in Lorentzian space. This allowed us to prove that φ(P)= ∏_(i=1)^n▒(1+εi rki ) In addition to Gaussian and mean curvatures, K_r and H_r for parallel surfaces in E_1^3 are given. In this study by means of higher order Gaussian and mean curvatures we calculate the generalized curvatures K_r and H_r for parallel surfaces in E_1^(n+1).
Keyword:Gaussian curvatures, mean curvatures, parallel hypersurfaces, higher order Gaussian curvatures.