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November 2013 Spacelike foliations by $(n−1)$-umbilical hypersurfaces in spacetimes
A. Gervasio Colares, Oscar Palmas
Asian J. Math. 17(4): 621-644 (November 2013).

Abstract

We consider the problem of whether a given spacetime admits a foliation by $(n−1)$-umbilical spacelike hypersurfaces. We introduce the notion of a timelike closed partially conformal vector field in a spacetime and show that the existence of a vector field of this kind guarantees in turn the existence of that foliation. We then construct explicit examples of families of $(n−1)$-umbilical spacelike hypersurfaces in the de Sitter space. Imposing the further condition of having constant $r$-th mean curvature, we give the complete description of any leaf of a foliation of the de Sitter space by these hypersurfaces. Finally, in a spacetime foliated by $(n−1)$-umbilical spacelike hypersurfaces we characterize the immersed spacelike hypersurfaces which are $(n−1)$-umbilical.

Citation

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A. Gervasio Colares. Oscar Palmas. "Spacelike foliations by $(n−1)$-umbilical hypersurfaces in spacetimes." Asian J. Math. 17 (4) 621 - 644, November 2013.

Information

Published: November 2013
First available in Project Euclid: 22 August 2014

zbMATH: 1286.53033
MathSciNet: MR3152257

Subjects:
Primary: 53C12
Secondary: 53A10

Rights: Copyright © 2013 International Press of Boston

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Vol.17 • No. 4 • November 2013
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