On space‐like class A$\mathcal {A}$ surfaces in Robertson–Walker spacetimes

Abstract

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