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 [Formula: see text], which are dependent on three parameters and possess a space-like axis in the Minkowski 4-space [Formula: see text]. We provide an in-depth analysis of the fundamental forms, Gauss map, and shape operator associated with [Formula: see text]. 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 [Formula: see text] satisfy the umbilical conditions. Lastly, we examine the Laplacian of hypersurfaces family in [Formula: see text], shedding light on its important properties.