CONSTANT CURVATURE SURFACES IN A PSEUDO-ISOTROPIC SPACE

Abstract

In this study, we deal with the local structure of curves and surfaces immersed in a pseudo-isotropic space I-p(3) that is a particular Cayley-Klein space. We provide the formulas of curvature, torsion and Frenet trihedron for spacelike and timelike curves, respectively. The causal character of all admissible surfaces in I-p(3) has to be timelike up to its absolute. We introduce the formulas of Gaussian and mean curvature for timelike surfaces in I-p(3). As applications, we describe the surfaces of revolution which are the orbits of a plane curve under a hyperbolic rotation with constant Gaussian and mean curvature.