On Space-Like Class a Surfaces in Robertson-Walker Space Times

Abstract

In recent years, there has been significant interest among geometers in studying submanifolds of product spaces resulting in numerous findings. Some of them are given by [5], [8], [3], [7], [6]. Apart from Cartesian product spaces, the other example can be considered as Robertson Walker-Space times which are 4-dimensional Lorentzian manifolds. The Robertson Walker- Space times, denoted by L41 (f, c), are defined as Cartesian products of space forms by a real interval equipped with a Lorentzian warped product metric. Thus, the family of Robertson Walker space times includes the de Sitter, Minkowski, and the anti-de Sitter space time and also Friedmann’s cosmological models. In physics, Robertson Walker-Space times are important due to the fact that they explain homogeneous, isotropic expanding and contracting universes, see [15] and [1].