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

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