Pseudo-Isotropic Centro-Affine Lorentzian Surfaces

Abstract

In this paper, we study centro-affine Lorentzian surfaces M2 in ℝ3 which have pseudo-isotropic or lightlike pseudo-isotropic difference tensor. We first show that M2 is pseudo-isotropic if and only if the Tchebychev form T=0. In that case, M2 is a an equi-affine sphere. Next, we will get a complete classification of centro-affine Lorentzian surfaces which are lightlike pseudo-isotropic but not pseudo-isotropic.