Surfaces in Robertson-Walker Space-Times with Positive Relative Nullity

Abstract

In this article, we study space-like and time-like surfaces in a Robertson-Walker space-time, denoted by L41 ( f , c), having positive relative nullity. First,we give the necessary and sufficient conditions for such space-like and time-like surfaces in L41 ( f , c). Then, we obtain the local classification theorems for space-like and time-like surfaces in L41 ( f , 0) with positive relative nullity, where the second factor is 3-dimensional Euclidean space. Finally, we consider the space-like and time-like surfaces in E11 ×S3 and E11 × H3 with positive relative nullity. These are the special spaces of L41( f , c) when the warping function f is a constant function, with c = 1 for E11 × S3 and c = −1 for E11 × H3.