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.