Integral inequalities for maximal space-like submanifolds in the indefinite space form (Q2770046)

Let \(M^n\) be an \(n\)-dimensional Riemannian manifold immersed in \(M_p^{n+p} (c)\), where \(M_p^{n+p}(c)\) is an \((n+p)\)-dimensional connected semi-Riemannian manifold of constant curvature \(c\). If the semi-Riemannian metric of \(M_p^{n+p} (c)\) induces the Riemannian metric on \(M^n\), \(M^n\) is called a space-like submanifold. Such a submanifold with vanishing mean curvature is called a maximal space-like submanifold. The author gives intrinsic integral inequalities for compact maximal space-like submanifolds and a sufficient and necessary condition for such a submanifold to be totally geodesic.