Generalized Helical Hypersurfaces Having Time-like Axis in Minkowski Spacetime

Abstract

In this paper, the generalized helical hypersurfaces x = x(u,v,w) with a time-like axis in Minkowski spacetime E-1(4) are considered. The first and the second fundamental form matrices, the Gauss map, and the shape operator matrix of x are calculated. Moreover, the curvatures of the generalized helical hypersurface x are obtained by using the Cayley-Hamilton theorem. The umbilical conditions for the curvatures of x are given. Finally, the Laplace-Beltrami operator of the generalized helical hypersurface with a time-like axis is presented in E-1(4).