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Integral inequalities for maximal space-like submanifolds in the indefinite space form. (English) Zbl 1060.53061

From the author’s abstract: We study compact maximal space-like submanifolds in the indefinite space form with flat normal bundle. We prove two intrinsic integral inequalities for such submanifolds, and give a necessary and sufficient condition for such a submanifold to be totally geodesic.

MSC:

53C40 Global submanifolds
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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