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 in order for spacelike and timelike curves. The causal character of all admissible surfaces in I_{p}^{3} has to be timelike or lightlike 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.

11 pages, 4 figures. All comments are welcome

Cited by in corpus (4)

• The geometry of Gauss map and shape operator in simply isotropic and pseudo-isotropic spaces
• Rotation minimizing frames and spherical curves in simply isotropic and pseudo-isotropic 3-spaces
• $d$-minimal surfaces in three-dimensional singular semi-Euclidean space ${\mathbb{R}}^{0,2,1}$
• Certain classifications on surfaces of revolution in a semi-isotropic space