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

In this paper, we consider space‐like surfaces in Robertson–Walker spacetimes L14(f,c)$L^4_1(f,c)$ with the comoving observer field ∂∂t$\frac{\partial }{\partial t}$. We study some problems related to such surfaces satisfying the geometric conditions imposed on the tangential and normal parts of the unit vector field ∂∂t$\frac{\partial }{\partial t}$, as naturally defined. First, we investigate space‐like surfaces in L14(f,c)$L^4_1(f,c)$ satisfying that the tangent component of ∂∂t$\frac{\partial }{\partial t}$ is an eigenvector of all shape operators, called class A$\mathcal {A}$ surfaces. Then, we get a classification theorem for space‐like class A$\mathcal {A}$ surfaces in L14(f,0)$L^4_1(f,0)$. Also, we examine minimal space‐like class A$\mathcal {A}$ surfaces in L14(f,0)$L^4_1(f,0)$. Finally, we give the parameterizations of space‐like surfaces in L14(f,0)$L^4_1(f,0)$ when the normal part of the unit vector field ∂∂t$\frac{\partial }{\partial t}$ is parallel.