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Mat. Zametki, 2009, Volume 86, Issue 5, Pages 776–793 (Mi mz8517)  

This article is cited in 1 scientific paper (total in 1 paper)

Nonnegative Sectional Curvature Hypersurfaces in a Real Space Form

Shichang Shua, Annie Yi Hanb

a Xianyang Normal University
b Borough of Manhattan Community College

Abstract: In this paper, we investigate the nonnegative sectional curvature hypersurfaces in a real space form $M^{n+1}(c)$. We obtain some rigidity results of nonnegative sectional curvature hypersurfaces $M^{n+1}(c)$ with constant mean curvature or with constant scalar curvature. In particular, we give a certain characterization of the Riemannian product $S^k(a)\times S^{n-k}(\sqrt{1-a^2})$, $1\le k\le n-1$, in $S^{n+1}(1)$ and the Riemannian product $H^k(\operatorname{tanh}^2r-1)\times S^{n-k}(\operatorname{coth}^2r-1)$, $1\le k\le n-1$, in $H^{n+1}(-1)$.

Keywords: hypersurface in Euclidean $n$-space, space form, mean curvature, scalar curvature, principal curvature, sectional curvature, umbilical sphere, Codazzi equation, Ricci identity

DOI: https://doi.org/10.4213/mzm8517

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English version:
Mathematical Notes, 2009, 86:5, 729–743

Bibliographic databases:

UDC: 514.74
Received: 30.07.2008

Citation: Shichang Shu, Annie Yi Han, “Nonnegative Sectional Curvature Hypersurfaces in a Real Space Form”, Mat. Zametki, 86:5 (2009), 776–793; Math. Notes, 86:5 (2009), 729–743

Citation in format AMSBIB
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\by Shichang Shu, Annie Yi Han
\paper Nonnegative Sectional Curvature Hypersurfaces in a Real Space Form
\jour Mat. Zametki
\yr 2009
\vol 86
\issue 5
\pages 776--793
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\crossref{https://doi.org/10.4213/mzm8517}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2641350}
\zmath{https://zbmath.org/?q=an:1184.53063}
\transl
\jour Math. Notes
\yr 2009
\vol 86
\issue 5
\pages 729--743
\crossref{https://doi.org/10.1134/S0001434609110157}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-73949115791}


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  • https://doi.org/10.4213/mzm8517
  • http://mi.mathnet.ru/eng/mz/v86/i5/p776

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Shu Shichang, “Linear Weingarten hypersurfaces in a real space form”, Glasg. Math. J., 52:3 (2010), 635–648  crossref  mathscinet  zmath  isi  scopus
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