Proceedings of the International Conference on Geometry, Integrability and Quantization

Some Estimates for the Curvatures of Spacelike Hypersurfaces in de Sitter Space

Juan A. Aledo and Luis J. Alías

Abstract

In this paper we will report on our recent studies on curvature properties of space-like hypersurfaces in de Sitter space. In particular, we will state certain estimates for the higher order mean curvatures, the scalar curvature and the Ricci curvature of complete space-like hypersurfaces in de Sitter space. We will also establish a sufficient condition for a compact space-like hypersurface in de Sitter space to be spherical in terms of a lower bound for the square of its mean curvature.

Article information

Source
Proceedings of the Second International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Gregory L. Naber, eds. (Sofia: Coral Press Scientific Publishing, 2001), 72-81

Dates
First available in Project Euclid: 5 June 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1433528465

Digital Object Identifier
doi:10.7546/giq-2-2001-72-81

Mathematical Reviews number (MathSciNet)
MR1815631

Zentralblatt MATH identifier
1082.53053

Citation

Aledo, Juan A.; Alías, Luis J. Some Estimates for the Curvatures of Spacelike Hypersurfaces in de Sitter Space. Proceedings of the Second International Conference on Geometry, Integrability and Quantization, 72--81, Coral Press Scientific Publishing, Sofia, Bulgaria, 2001. doi:10.7546/giq-2-2001-72-81. https://projecteuclid.org/euclid.pgiq/1433528465


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