CLASSIFICATION THEOREMS FOR SPACE-LIKE SURFACES IN 4-DIMENSIONAL INDEFINITE SPACE FORMS WITH INDEX 2

Surfaces in 4D Riemannian space forms have been investigated extensively. In contrast, only few results are known for surfaces in 4D neutral indefinite space forms R-2(4)(c). Thus, in this paper we study space-like surfaces in R-2(4)(c) satisfying certain simple geometric properties. In particular, we classify space-like surfaces in E-2(4) with constant mean and Gauss curvatures and null normal curvature. We also classify Wintgen ideal surfaces in R-2(4)(c) whose Gauss and normal curvatures satisfy K-D = 2K.