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Constant Mean Curvature Spacelike Hypersurfaces in Spacetimes with Certain Causal Symmetries

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Hermitian–Grassmannian Submanifolds

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 203))

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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Acknowledgements

Research partially supported by Spanish MINECO and ERDF project MTM2013-47828-C2-1-P. The author would like to express his deep and sincere thanks to the organizers of the 20th International Workshop on Hermitian Symmetric Spaces and Submanifolds and the 12th RIRCM-OCAMI Joint Differential Geometry Workshop, held in Kyungpook National University, Daegu (Korea), July 26–30, 2016, specially to Professor Young Jin Suh for the support for his participation in the congress and the warm hospitality during his stay in Korea, and to Dr. Hyunjin Lee and Mr. Changhwa Woo for their kindness and the excellent work done as the congress secretariat.

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Authors and Affiliations

  1. Departamento de Geometría y Topología, Universidad de Granada, 18071, Granada, Spain

    Alfonso Romero

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  1. Alfonso Romero
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Correspondence to Alfonso Romero .

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Editors and Affiliations

  1. Department of Mathematics and RIRCM, Kyungpook National University , Daegu, Korea (Republic of)

    Young Jin Suh

  2. Department of Mathematics and OCAMI, Osaka City University, Osaka, Japan

    Yoshihiro Ohnita

  3. School of Mathematics and Statistics, Southwest University, Chongqing, China

    Jiazu Zhou

  4. Department of Applied Mathematics, Kyung Hee University, Gyeonggi, Korea (Republic of)

    Byung Hak Kim

  5. Research Institute of Real and Complex Manifolds (RIRCM), Kyungpook National University, Daegu, Korea (Republic of)

    Hyunjin Lee

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Romero, A. (2017). Constant Mean Curvature Spacelike Hypersurfaces in Spacetimes with Certain Causal Symmetries. In: Suh, Y., Ohnita, Y., Zhou, J., Kim, B., Lee, H. (eds) Hermitian–Grassmannian Submanifolds. Springer Proceedings in Mathematics & Statistics, vol 203. Springer, Singapore. https://doi.org/10.1007/978-981-10-5556-0_1

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