Bulletin of the Belgian Mathematical Society - Simon Stevin

Rigidity theorem for complete spacelike submanifold in $S^{n+p}_q(1)$ with constant scalar curvature

Shicheng Zhang

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Abstract

In this paper, the complete spacelike submanifold with parallel normalized mean curvature vector and constant normalized scalar curvature is discussed in $(n+p)$-dimensional connected semi-Riemannian manifold $S^{n+p}_q(1)$ $(1\leq q\leq p)$ and a rigidity theorem is obtained.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 4 (2012), 733-746.

Dates
First available in Project Euclid: 23 November 2012

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1353695912

Digital Object Identifier
doi:10.36045/bbms/1353695912

Mathematical Reviews number (MathSciNet)
MR3009033

Zentralblatt MATH identifier
1262.53052

Subjects
Primary: 53C24: Rigidity results 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42] 53C50: Lorentz manifolds, manifolds with indefinite metrics

Keywords
semi-Riemannian manifold spacelike submanifold constant normalized scalar curvature

Citation

Zhang, Shicheng. Rigidity theorem for complete spacelike submanifold in $S^{n+p}_q(1)$ with constant scalar curvature. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 4, 733--746. doi:10.36045/bbms/1353695912. https://projecteuclid.org/euclid.bbms/1353695912


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