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Anti-De Sitter Spacetimes and Isoparametric Hypersurfaces in Complex Hyperbolic Spaces

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Lorentzian Geometry and Related Topics (GELOMA 2016)

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Abstract

By lifting hypersurfaces in complex hyperbolic spaces to anti-De Sitter spacetimes, we prove that an isoparametric hypersurface in the complex hyperbolic space has the same principal curvatures as a homogeneous one.

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Acknowledgements

The authors have been supported by projects MTM2016-75897-P (AEI/FEDER, UE), ED431F 2017/03, GRC2013-045 and MTM2013-41335-P with FEDER funds (Spain). The second author has received funding from a Juan de la Cierva fellowship (Spain), from the ICMAT Severo Ochoa project SEV-2015-0554 (MINECO, Spain), and from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 745722. The third author has been supported by an FPU fellowship and by Fundación Barrié de la Maza (Spain).

Author information

Authors and Affiliations

  1. Department of Mathematics, Universidade de Santiago de Compostela, Santiago, Spain

    J. Carlos Díaz-Ramos & Víctor Sanmartín-López

  2. ICMAT - Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Madrid, Spain

    Miguel Domínguez-Vázquez

Authors
  1. J. Carlos Díaz-Ramos
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  2. Miguel Domínguez-Vázquez
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  3. Víctor Sanmartín-López
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Corresponding author

Correspondence to J. Carlos Díaz-Ramos .

Editor information

Editors and Affiliations

  1. Department of Algebra, Geometry, Topology, University of Malaga, Málaga, Spain

    María A. Cañadas-Pinedo

  2. Department of Algebra, Geometry, Topology, University of Malaga, Málaga, Spain

    José Luis Flores

  3. Department of Applied Mathematics, University of Malaga, Malaga, Spain

    Francisco J. Palomo

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Díaz-Ramos, J.C., Domínguez-Vázquez, M., Sanmartín-López, V. (2017). Anti-De Sitter Spacetimes and Isoparametric Hypersurfaces in Complex Hyperbolic Spaces. In: Cañadas-Pinedo, M., Flores, J., Palomo, F. (eds) Lorentzian Geometry and Related Topics. GELOMA 2016. Springer Proceedings in Mathematics & Statistics, vol 211. Springer, Cham. https://doi.org/10.1007/978-3-319-66290-9_6

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