Rotational hypersurfaces in Lorentz-Minkowski 4-space

Abstract

In this study, we study rotational hypersurfaces in 4-dimensional Lorentz-Minkowski space. We find the rotational hypersurfaces about spacelike axis according to Gaussian and mean curvatures in E 4 1 and give some results with the aid of the Gaussian and mean curvatures. After that, we deal with the Gauss map of rotational hypersurface about spacelike axis by obtaining the Gaussian and mean curvatures. We obtain the second and third Laplace-Beltrami operators on rotational hypersurface about spacelike axis in E 4 1 . Also, we give these characterizations for rotational hypersurfaces about timelike and lightlike axes, too.

A New Approach to Timelike Hypersurfaces of Constant Ratio in I E 1 4 Büyükkütük 2023Journal of Mathematics1000View full textAdd to dashboardCite

“…In four-dimensional Minkowski space, with the help of spacelike, timelike, and lightlike axis spanned by (0, 0, 0, 1), (1, 0, 0, 0), and (1, 1, 0, 0), the three rotation matrices are given by [11]…”

Canal hypersurfaces according to one of the extended Darboux frame field in Euclidean 4-space

“…Furthermore, the differential geometry of different types of (hyper)surfaces in 4-D spaces has been a popular topic for geometers, recently, [17,[28][29][30][31][32][33][34][35], and etc. If Ω: U ⊂ E 3 → E 4 is a hypersurface in E 4 parametrized by: ( )…”