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Equigeodesics on Generalized Flag Manifolds with Two Isotropy Summands

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Abstract

In this paper we study homogeneous curves in generalized flag manifolds with two isotropy summands with the additional property that such curves are geodesics with respect to each invariant metric on the flag manifold. These curves are called equigeodesics. We give an algebraic characterization for such curves and we exhibit families of equigeodesics in several flag manifolds of classical and exceptional Lie groups.

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Authors and Affiliations

  1. Department of Mathematics, Institute of Mathematics, Statistics and Scientific Computation, University of Campinas, UNICAMP, P. O. Box 6065, São Paulo, Brazil

    Lino Grama & Caio J. C. Negreiros

Authors
  1. Lino Grama
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  2. Caio J. C. Negreiros
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Corresponding author

Correspondence to Lino Grama.

Additional information

Dedicated to Professor Keti Tenenblat on the occasion of her 65th birthday.

Research supported by FAPESP grant no. 07/06896-5, CAPES/CNPq grant no. 140431/2009-8.

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Grama, L., Negreiros, C.J.C. Equigeodesics on Generalized Flag Manifolds with Two Isotropy Summands. Results. Math. 60, 405–421 (2011). https://doi.org/10.1007/s00025-011-0149-2

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  • DOI: https://doi.org/10.1007/s00025-011-0149-2

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