  Let $M$ be a space-like surface immersed in a 4-dimensional pseudo-Riemannian
space form $R^4_2(c)$ with constant sectional curvature $c$ and index two. In
the first part of this article, we prove that the Gauss curvature $K$, the
normal curvature $K^D$, and mean curvature vector $H$ of $M$ satisfy the
general inequality: $K+K^D\geq H,H +c$. In the second part, we investigate
space-like minimal surfaces in $R^4_2(c)$ which satisfy the equality case of
the inequality identically. Several classification results in this respect are
then obtained.
