THE RICCI FLOW FOR NILMANIFOLDS

被引：20

作者：

Payne, Tracy L. ^{[1
]}

机构：

[1] Idaho State Univ, Dept Math, Pocatello, ID 83209 USA

来源：

JOURNAL OF MODERN DYNAMICS | 2010年 / 4卷 / 01期

关键词：

nilmanifold; Ricci flow; soliton metric; GEOMETRIES;

D O I：

10.3934/jmd.2010.4.65

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Ricci flow for simply connected nilmanifolds. This translates to a Ricci flow on the space of nilpotent metric Lie algebras. We consider the evolution of the inner product and the evolution of structure constants, as well as the evolution of these quantities modulo rescaling. We set up systems of O.D.E.'s for some of these flows and describe their qualitative properties. We also present some explicit solutions for the evolution of soliton metrics under the Ricci flow.

引用

页码：65 / 90

页数：26

共 18 条

[1] GLICKENSTEIN D, ARXIV09090938
[2] Linear stability of homogeneous Ricci solitons
Guenther, Christine
Isenberg, James
Knopf, Dan
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2006, 2006
[3] GUZHVINA G, 2007, THESIS W FALISCHE WI
[4] HAMILTON RS, 1982, J DIFFER GEOM, V17, P255
[5] Noncompact homogeneous Einstein spaces
Heber, J
[J]. INVENTIONES MATHEMATICAE, 1998, 133 (02) : 279 - 352
[6] ISENBERG J, 1992, J DIFFER GEOM, V35, P723
[7] Isenberg J, 2006, COMMUN ANAL GEOM, V14, P345
[8] JABLONSKI M, ARXIV08063721
[9] Jensen Gary R., 1969, J. Differential Geometry, V3, P309, DOI 10.4310/jdg/1214429056
[10] Quasi-convergence of model geometries under the Ricci flow
Knopf, D
McLeod, K
[J]. COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2001, 9 (04) : 879 - 919

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