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

Author(s)

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

Affiliation

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

• Document type: Journal article
• Source: BULLETIN DES SCIENCES MATHEMATIQUES; v. 133, n. 5, p. 463-469, JUL 2009.
• Web of Science Citations: 6

Abstract

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)

• FAPESP's process: 07/05215-4 - The Hamiltonian structure of normal forms for elliptic equilibria of reversible vector fields in 4D and 6D
• Grantee: Ricardo Miranda Martins
• Support Opportunities: Scholarships in Brazil - Doctorate