Twisted hypersurfaces family with a space-like axis in Minkowski 4-space

Abstract

We present an exploration of helical or twisted hypersurfaces family denoted as x, which are dependent on three parameters and possess a space-like axis in the Minkowski 4-space ???4. We provide an in-depth analysis of the fundamental forms, Gauss map, and shape operator associated with x. We establish a framework for defining the curvatures of any given family using the Cayley-Hamilton theorem. By applying this theorem, we derive the specific curvatures of the hypersurface under consideration. Furthermore, we investigate the conditions under which the curvatures of x satisfy the umbilical conditions. Lastly, we examine the Laplacian of hypersurfaces family in ???4, shedding light on its important properties.