The Ricci curvature of finite dimensional approximations to loop and path groups

被引：0

作者：

Cecil, Matthew ^{[1
]}

机构：

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2009年 / 133卷 / 04期

关键词：

Path group; Loop group; Ricci curvature; QUASI-INVARIANCE; SPACE;

D O I：

10.1016/j.bulsci.2008.10.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let W(G) and C(G) denote the path and loop groups respectively of a connected real unimodular Lie group G endowed with a left-invariant Riemannian metric. We study the Ricci curvature of certain finite dimensional approximations to these groups based on partitions of the interval vertical bar 0, 1 vertical bar. We find that the Ricci curvatures of the finite dimensional approximations are bounded below independent of partition iff G is of compact type with an Ad-invariant metric. (C) 2008 Elsevier Masson SAS. All rights reserved.

引用

页码：383 / 405

页数：23

共 30 条

[11] Ricci Curvature of Finite Markov Chains via Convexity of the Entropy
Matthias Erbar
Jan Maas
Archive for Rational Mechanics and Analysis, 2012, 206 : 997 - 1038
[12] Convergence of finite dimensional distributions of heat kernel measures on loop groups
Inahama, Y
JOURNAL OF FUNCTIONAL ANALYSIS, 2003, 198 (02) : 311 - 340
[13] Negative Ricci curvature on some non-solvable Lie groups
Will, Cynthia E.
GEOMETRIAE DEDICATA, 2017, 186 (01) : 181 - 195
[14] Negative Ricci curvature on some non-solvable Lie groups
Cynthia E. Will
Geometriae Dedicata, 2017, 186 : 181 - 195
[15] Three-Dimensional Alexandrov Spaces with Positive or Nonnegative Ricci Curvature
Qintao Deng
Fernando Galaz-García
Luis Guijarro
Michael Munn
Potential Analysis, 2018, 48 : 223 - 238
[16] Three-Dimensional Alexandrov Spaces with Positive or Nonnegative Ricci Curvature
Deng, Qintao
Galaz-Garcia, Fernando
Guijarro, Luis
Munn, Michael
POTENTIAL ANALYSIS, 2018, 48 (02) : 223 - 238
[17] The signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional Lie groups. The nonunimodular case
Kremlev A.G.
Nikonorov Y.G.
Siberian Advances in Mathematics, 2010, 20 (1) : 1 - 57
[18] The signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional lie groups. The unimodular case
Kremlev A.G.
Nikonorov Y.G.
Siberian Advances in Mathematics, 2009, 19 (4) : 245 - 267
[19] Isoperimetric inequalities for finite perimeter sets under lower Ricci curvature bounds
Cavalletti, Fabio
Mondino, Andrea
RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI, 2018, 29 (03) : 413 - 430
[20] On the four-dimensional T2-manifolds of positive Ricci curvature
Ya. V. Bazaikin
I. V. Matvienko
Siberian Mathematical Journal, 2007, 48 : 778 - 783

← 1 2 3 →