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Let N%+P(c) be a (2+£)-dimensional connected indefinite Riemannian manifold of index p and of constant curvature c, which is called an indefinite space form of index p. According to c>0, c=0 or c<0, it is a pseudo-Riemannian sphere S2p+P(c),a pseudo-Euclidean space R2P+P or a pseudo-Hyperbolic space H2p+P(c),respectively. A surface M of an indefinite space form NP+p(c) is said to be space-like if the induced metric on M from that of N%+P(c) is positive definite. Suppose M is a space-like surface with parallel mean curvature vector H in an indefinite space form N2p+P(c). Let K be the Gauss curvature of M and H― |H\. We remark that the square norm S of the second fundamental form of M satisfiesthe following Gauss equation (see (2.6))

On space-like surfaces with parallel mean curvature vector of an indefinite space form