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

2012/03/21 by J. C. González-Dávila, González-Dávila, J. C., A. M. Naveira +1
Mathematics · #53C20 #53C22 #53C30 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C20 #msc:53C22 #msc:53C30

paper · pdf · doi:10.48550/arxiv.1203.4676

arxiv created 2012/03/21 · arxiv updated 2012/03/22

Abstract

We give a positive answer to the Chavel's conjecture [J. Diff. Geom. 4 (1970), 13-20]: 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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