Spectral isolation of naturally reductive metrics on simple Lie groups

被引：6

作者：

Gordon, Carolyn S. ^{[1
]}

Sutton, Craig J. ^{[1
]}

机构：

[1] Dartmouth Coll, Dept Math, Hanover, NH 03755 USA

来源：

MATHEMATISCHE ZEITSCHRIFT | 2010年 / 266卷 / 04期

基金：

美国国家科学基金会;

关键词：

Laplacian; Eigenvalue spectrum; Naturally reductive metrics; Symmetric spaces; FLAT TORI; MANIFOLDS; RIGIDITY; EIGENVALUE; LAPLACIAN;

D O I：

10.1007/s00209-009-0640-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that within the class of left-invariant naturally reductive metrics M(Nat)(G) on a compact simple Lie group G, every metric is spectrally isolated. We also observe that any collection of isospectral compact symmetric spaces is finite; this follows from a somewhat stronger statement involving only a finite part of the spectrum.

引用

页码：979 / 995

页数：17

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