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Real Hypersurfaces with Two Principal Curvatures in Complex Projective and Hyperbolic Planes

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Abstract

We find the first examples of real hypersurfaces with two nonconstant principal curvatures in complex projective and hyperbolic planes, and we classify them. It turns out that each such hypersurface is foliated by equidistant Lagrangian flat surfaces with parallel mean curvature or, equivalently, by principal orbits of a cohomogeneity two polar action.

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Acknowledgments

The authors would like to thank Professors Jürgen Berndt and Tillmann Jentsch for helpful observations and comments.

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Authors and Affiliations

  1. Department of Geometry and Topology, University of Santiago de Compostela, Santiago de Compostela, Spain

    José Carlos Díaz-Ramos & Cristina Vidal-Castiñeira

  2. Instituto de Ciencias Matemáticas (ICMAT), Madrid, Spain

    Miguel Domínguez-Vázquez

Authors
  1. José Carlos Díaz-Ramos
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  2. Miguel Domínguez-Vázquez
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  3. Cristina Vidal-Castiñeira
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Corresponding author

Correspondence to José Carlos Díaz-Ramos.

Additional information

Supported by projects EM2014/009, GRC2013-045 and MTM2013-41335-P with FEDER funds (Spain).

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Díaz-Ramos, J.C., Domínguez-Vázquez, M. & Vidal-Castiñeira, C. Real Hypersurfaces with Two Principal Curvatures in Complex Projective and Hyperbolic Planes. J Geom Anal 27, 442–465 (2017). https://doi.org/10.1007/s12220-016-9686-y

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  • DOI: https://doi.org/10.1007/s12220-016-9686-y

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