Generalized Helical Hypersurface with Space-like Axis in Minkowski 5-Space

Abstract

We introduce the generalized helical hypersurface having a space-like axis in five-dimensional Minkowski space. We compute the first and second fundamental form matrices, Gauss map, and shape operator matrix of the hypersurface. Additionally, we compute the curvatures of the hypersurface by using the Cayley–Hamilton theorem. Moreover, we give some relations for the mean and the Gauss–Kronecker curvatures of the hypersurface. Finally, we obtain the Laplace–Beltrami operator of the hypersurface.

Keywords

• Minkowski 5-space
• Lorentzian inner product
• Lorentzian quadruple vector product
• helical hypersurface
• Gauss map
• curvature