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Annals of Global Analysis and Geometry

, Volume 55, Issue 3, pp 451–477 | Cite as

Variational aspects of homogeneous geodesics on generalized flag manifolds and applications

  • Rafaela F. do Prado
  • Lino GramaEmail author
Article
  • 85 Downloads

Abstract

We study conjugate points along homogeneous geodesics in generalized flag manifolds. This is done by analyzing the second variation of the energy of such geodesics. We also give an example of how the homogeneous Ricci flow can evolve in such way to produce conjugate points in the complex projective space \({\mathbb {C}}P^{2n+1} = \text {Sp}(n+1)/(\text {U}(1)\times \text {Sp}(n))\).

Keywords

Geometry of homogeneous space Homogeneous geodesics Conjugate points Morse index Generalized flag manifolds 

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Mathematics - IMECCUniversity of CampinasCampinasBrazil
  2. 2.Federal Institute of Brasília - IFB - Campus GamaBrasíliaBrazil

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