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Foliations by Spacelike Hypersurfaces on Lorentz Manifolds

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Abstract

In this work, we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We find an equation that relates the foliation with the ambient manifold and applies it to investigate conditions for the leaves being totally umbilical or geodesic. Using the Maximum principle with the mentioned equation we obtain an obstruction for the existence of totally geodesic spacelike foliations in a spacetime with positive Ricci curvature on the direction N.

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Acknowledgements

Both authors are grateful to Antonio Caminha for interesting and useful discussions. This work was carried out during their visit in 2018 and 2019 a visit at Universidade Federal do Ceará.

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Authors and Affiliations

  1. Instituto Federal de Educação, Ciência e Tecnologia do Ceará, Avenida Parque Central, 1315, Maracanaú, Ceará, 61939-140, Brazil

    Euripedes Carvalho da Silva

  2. Departamento de Matemática, Universidade de São Paulo, Rua do Matão, 1010, São Paulo, 05508-090, Brazil

    Rosa Maria dos Santos Barreiro Chaves

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  1. Rosa Maria dos Santos Barreiro Chaves
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  2. Euripedes Carvalho da Silva
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Correspondence to Euripedes Carvalho da Silva.

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Chaves, R.M.d.S.B., da Silva, E.C. Foliations by Spacelike Hypersurfaces on Lorentz Manifolds. Results Math 75, 36 (2020). https://doi.org/10.1007/s00025-020-1159-8

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  • DOI: https://doi.org/10.1007/s00025-020-1159-8

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