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Published in:
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2017 | OriginalPaper | Chapter

Constant Mean Curvature Spacelike Hypersurfaces in Spacetimes with Certain Causal Symmetries

Author : Alfonso Romero

Published in: Hermitian–Grassmannian Submanifolds

Publisher: Springer Singapore

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Abstract

The role of some causal symmetries of spacetime which naturally arise in General Relativity is discussed. The importance of spacelike hypersurfaces of constant mean curvature (CMC) in the study of the Einstein equation is recalled. In certain spacetimes with symmetry defined by a timelike gradient conformal vector field or by a lightlike parallel vector field, uniqueness theorems of complete CMC spacelike hypersurfaces are given. In several cases, results of Calabi–Bernstein type are obtained as an application.

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next chapter Sequences of Maximal Antipodal Sets of Oriented Real Grassmann Manifolds II
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Metadata
Title
Constant Mean Curvature Spacelike Hypersurfaces in Spacetimes with Certain Causal Symmetries
Author
Alfonso Romero
Copyright Year
2017
Publisher
Springer Singapore
Book
Hermitian–Grassmannian Submanifolds

Print ISBN: 978-981-10-5555-3

Electronic ISBN: 978-981-10-5556-0

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-981-10-5556-0_1

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