The Ricci flow of left-invariant metrics on full flag manifold SU(3)/T from a dynamical systems point of view

Autor(es)

Grama, Lino ^[1] ; Martins, Ricardo Miranda ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, UNICAMP, Dept Math, Inst Math Stat & Sci Comp, Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: BULLETIN DES SCIENCES MATHEMATIQUES; v. 133, n. 5, p. 463-469, JUL 2009.
• Citações Web of Science: 6

Resumo

In this paper we study the behavior of the Ricci flow at infinity for the full flag manifold SU(3)IT using techniques of the qualitative theory of differential equations, in special the Poincare compactification and Lyapunov exponents. We prove that there are four invariant lines for the Ricci flow equation, each one associated with a singularity corresponding to an Einstein metric. In such manifold, the bi-invariant normal metric is Einstein. Moreover, around each invariant line there is a cylinder of initial conditions such that the limit metric under the Ricci flow is the corresponding Einstein metric; in particular we obtain the convergence of left-invariant metrics to a bi-invariant metric under the Ricci flow. (C) 2009 Elsevier Masson SAS. All rights reserved. (AU)

• Processo FAPESP: 07/05215-4 - Estrutura Hamiltoniana de campos reversíveis em torno de pontos de equilíbrio elípticos em 4D e 6D
• Beneficiário: Ricardo Miranda Martins
• Modalidade de apoio: Bolsas no Brasil - Doutorado