Bulletin of the Belgian Mathematical Society - Simon Stevin

Spacelike hypersurfaces with nonzero constant $\boldsymbol{k}$-th mean curvature and two distinct principal curvatures in anti-de Sitter spaces

Jiancheng Liu and Yan Wei

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Abstract

In this paper, we investigate the spacelike hypersurfaces in anti-de Sitter space $\mathbb{H}^{n+1}_1(c)$ with nonzero constant $k$-th mean curvature $H_k$ and two distinct principal curvatures one of which is simple, and characterize such hypersurfaces as hyperbolic cylinders.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 21, Number 1 (2014), 39-50.

Dates
First available in Project Euclid: 11 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1394544293

Digital Object Identifier
doi:10.36045/bbms/1394544293

Mathematical Reviews number (MathSciNet)
MR3178529

Zentralblatt MATH identifier
1287.53013

Subjects
Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]

Keywords
Anti-de Sitter space Spacelike hypersurface $k$-th mean curvature Principal curvatures Hyperbolic cylinder

Citation

Liu, Jiancheng; Wei, Yan. Spacelike hypersurfaces with nonzero constant $\boldsymbol{k}$-th mean curvature and two distinct principal curvatures in anti-de Sitter spaces. Bull. Belg. Math. Soc. Simon Stevin 21 (2014), no. 1, 39--50. doi:10.36045/bbms/1394544293. https://projecteuclid.org/euclid.bbms/1394544293


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