L1-2-Type Surfaces in 3-Dimensional De Sitter and Anti De Sitter Spaces

Let M-s(2) be an orientable surface immersed in the De Sitter space S-1(3) ? R-1(4) or anti de Sitter space H-1(3) ? R-2(4). In the case that M-s(2) is of L-1-2-type we prove that the following conditions are equivalent to each other: M-s(2) has a constant principal curvature; M-s(2) has constant mean curvature; M-s(2) has constant second mean curvature. As a consequence, we also show that an L-1-2-type surface is either an open portion of a standard pseudo Riemannian product, or a B-scroll over a null curve, or else its mean curvature, its Gaussian curvature and its principal curvatures are all non-constant.