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Spacelike submanifolds in the de Sitter space S p n+p (c) with constant scalar curvature

Spacelike submanifolds in the de Sitter space S p n+p (c) with constant scalar curvature Let M n be a closed spacelike submanifold isometrically immersed in de Sitter space S p n+p (c). Denote by R, H and S the normalized scalar curvature, the mean curvature and the square of the length of the second fundamental form of M n, respectively. Suppose R is constant and R≤c. The pinching problem on S is studied and a rigidity theorem for M n immersed in S p n+p (c) with parallel normalized mean curvature vector field is proved. When n≥3, the pinching constant is the best. Thus, the mistake of the paper “Space-like hypersurfaces in de Sitter space with constant scalar curvature” (see Manus Math, 1998, 95:499\s-505) is corrected. Moreover, the reduction of the codimension when M n is a complete submanifold in S p n+p (c) with parallel normalized mean curvature vector field is investigated. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics-A Journal of Chinese Universities Springer Journals

Spacelike submanifolds in the de Sitter space S p n+p (c) with constant scalar curvature

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Publisher
Springer Journals
Copyright
Copyright © 2005 by Editorial Committee of Applied Mathematics-A Journal of Chinese Universities
Subject
Mathematics; Mathematics, general; Applications of Mathematics
ISSN
1005-1031
eISSN
1993-0445
DOI
10.1007/s11766-005-0051-3
Publisher site
See Article on Publisher Site

Abstract

Let M n be a closed spacelike submanifold isometrically immersed in de Sitter space S p n+p (c). Denote by R, H and S the normalized scalar curvature, the mean curvature and the square of the length of the second fundamental form of M n, respectively. Suppose R is constant and R≤c. The pinching problem on S is studied and a rigidity theorem for M n immersed in S p n+p (c) with parallel normalized mean curvature vector field is proved. When n≥3, the pinching constant is the best. Thus, the mistake of the paper “Space-like hypersurfaces in de Sitter space with constant scalar curvature” (see Manus Math, 1998, 95:499\s-505) is corrected. Moreover, the reduction of the codimension when M n is a complete submanifold in S p n+p (c) with parallel normalized mean curvature vector field is investigated.

Journal

Applied Mathematics-A Journal of Chinese Universities – Springer Journals

Published: Jun 28, 2005

References

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    O’Neil, B
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