Journal of Mathematical Physics vol:48 issue:7 pages:073509
Let L^4_1(f,c)=(I ×_f S,g^c_f) be a Robertson-Walker space time which does not contain any open subset of constant curvature. In this paper, we provide a general study of nondegenerate surfaces in L^4_1(f,c). First, we prove the nonexistence of marginally trapped surfaces with positive relative nullity. Then, we classify totally geodesic submanifolds. Finally, we classify the family of surfaces with parallel second fundamental form and the family of totally umbilical surfaces with parallel mean curvature vector.