On Space-like Class A Surfaces in Robertson-Walker Space Times

In this article, we consider space-like surfaces in Robertson-Walker Space times L⁴₁(f,c) with comoving observer field ∂/∂ 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 ∂/∂ t naturally defined. First, we investigate space-like surfaces in L⁴₁(f,c) satisfying that the tangent component of ∂/∂ 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 L⁴₁(f,0). Also, we examine minimal space-like class A surfaces in L⁴₁(f,0). Finally, we give the parametrizations of space-like surfaces in L⁴₁(f,0) when the normal part of the unit vector field ∂/∂ t is parallel.