Variational results on flag manifolds: Harmonic maps, geodesics and Einstein metrics

Author(s)

Negreiros, Caio J. C. ^[1] ; Grama, Lino ^[1] ; da Silva, Neiton P. ^[2]

Affiliation

^[1] Univ Campinas UNICAMP, Inst Math Stat & Sci Computat, BR-13083859 Campinas, SP - Brazil

^[2] Univ Fed Uberlandia, Dept Math, BR-38408100 Uberlandia, MG - Brazil

• Document type: Journal article
• Source: Journal of Fixed Point Theory and Applications; v. 10, n. 2, p. 307-325, DEC 2011.
• Web of Science Citations: 0

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. (AU)

• FAPESP's process: 07/06896-5 - Geometry of control, dynamical and stochastic systems
• Grantee: Luiz Antonio Barrera San Martin
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 10/17034-7 - Differential geometry on homogeneous spaces
• Grantee: Lino Anderson da Silva Grama
• Support Opportunities: Scholarships in Brazil - Post-Doctoral