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Existence of non-isotropic conjugate points on rank one normal homogeneous spaces

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Abstract

We give a positive answer to the Chavel’s conjecture (J Differ Geom 4:13–20, 1970): a simply connected rank one normal homogeneous space is symmetric if any pair of conjugate points are isotropic. It implies that all simply connected rank one normal homogeneous space with the property that the isotropy action is variational complete is a rank one symmetric space.

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Acknowledgments

This study has been supported by D.G.I. (Spain) and FEDER Project MTM2010-15444. Also A. M. Naveira has been partially supported by the Generalitat Valenciana Project Prometeo 2009/099.

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Authors and Affiliations

  1. Department of Fundamental Mathematics, University of La Laguna, 38200 , La Laguna, Tenerife, Spain

    J. C. González-Dávila

  2. Department of Geometry and Topology, University of Valencia, 46100 , Burjassot, Valencia, Spain

    A. M. Naveira

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  1. J. C. González-Dávila
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  2. A. M. Naveira
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Correspondence to J. C. González-Dávila.

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González-Dávila, J.C., Naveira, A.M. Existence of non-isotropic conjugate points on rank one normal homogeneous spaces. Ann Glob Anal Geom 45, 211–231 (2014). https://doi.org/10.1007/s10455-013-9395-8

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  • DOI: https://doi.org/10.1007/s10455-013-9395-8

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