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

In this paper, we consider space-like surfaces in Robertson–Walker spacetimes (Formula presented.) with the comoving observer field (Formula presented.). We study some problems related to such surfaces satisfying the geometric conditions imposed on the tangential and normal parts of the unit vector field (Formula presented.), as naturally defined. First, we investigate space-like surfaces in (Formula presented.) satisfying that the tangent component of (Formula presented.) is an eigenvector of all shape operators, called class (Formula presented.) surfaces. Then, we get a classification theorem for space-like class (Formula presented.) surfaces in (Formula presented.). Also, we examine minimal space-like class (Formula presented.) surfaces in (Formula presented.). Finally, we give the parameterizations of space-like surfaces in (Formula presented.) when the normal part of the unit vector field (Formula presented.) is parallel.