3-dimensional space-like submanifolds with parallel mean curvature vector of an indefinite space form. II (Q1345356)

[Part I, cf. Kodai Math. J. 15, No. 2, 279-295 (1992; Zbl 0787.53047.] A submanifold of a pseudo-Riemannian manifold is said to be space-like if the metric on it induces from the ambient space is positive definite. In the present paper complete space-like 3-dimensional submanifolds \(M\) of the indefinite space form \(M^{3 + p}_p (c)\) with parallel mean curvature vector are studied. If the Ricci curvature of \(M\) is bounded from above by some number less than \(3(c - H^2)\), where \(H\) is the mean curvature of \(M\), then \(c > 0\) and \(M\) is congruent to a Riemannian 3-sphere. This is a generalization of a result of \textit{R. Aiyama} and \textit{Q.-M. Cheng} [Kodai Math. J. 15, No. 3, 375-386 (1992; Zbl 0777.53058)].