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

被引：9

作者：

Grama, Lino ^{[1
]}

Martins, Ricardo Miranda ^{[1
]}

机构：

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

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2009年 / 133卷 / 05期

基金：

巴西圣保罗研究基金会;

关键词：

Flag manifolds; Ricci flow; Left-invariant metric; Poincare compactification; CURVATURE;

D O I：

10.1016/j.bulsci.2009.05.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：463 / 469

页数：7