Variational results on flag manifolds: Harmonic maps, geodesics and Einstein metrics |
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Authors: | Caio J. C. Negreiros Lino Grama Neiton P. da Silva |
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Affiliation: | 1. Institute of Mathematics, Statistics and Scientific Computation, University of Campinas - UNICAMP, Campinas, S?o Paulo, CEP 13083-859, Brazil 2. Department of Mathematics, Universidade Federal de Uberlandia - UFU, Uberlandia - Minas Gerais, CEP 38.408-100, Brazil
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Abstract: | In this paper, we study variational aspects for harmonic maps from M to several types of flag manifolds and the relationship with the rich Hermitian geometry of these manifolds. We consider maps that are harmonic with respect to any invariant metric on each flag manifold. They are called equiharmonic maps. We survey some recent results for the case where M is a Riemann surface or is one dimensional; i.e., we study equigeodesics on several types of flag manifolds. We also discuss some results concerning Einstein metrics on such manifolds. |
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