On space-like class A surfaces in Robertson-Walker spacetimes

Abstract

In this article, we consider space-like surfaces in Robertson-Walker Space times L-1(4)(f,c) with comoving observer field (partial derivative)(partial derivative t). We study some problems related to such surfaces satisfying the geometric conditions imposed on the tangential part and normal part of the unit vector field (partial derivative)(partial derivative t) naturally defined. First, we investigate space-like surfaces in L-1(4)(f,c) satisfying that the tangent component of partial derivative partial derivative t is an eigenvector of all shape operators, called class A surfaces. Then, we get a classification theorem of space-like class A surfaces in L-1(4)(f,0). Also, we examine minimal space-like class A surfaces in L-1(4)(f,0). Finally, we give the parametrizations of space-like surfaces in L-1(4)(f,0) when the normal part of the unit vector field (partial derivative)(partial derivative t) is parallel.