Spectral isolation of naturally reductive metrics on simple Lie groups

Carolyn S. Gordon; Craig J. Sutton

doi:10.1007/s00209-009-0640-6

Spectral isolation of naturally reductive metrics on simple Lie groups

Differential Geometry 2010-06-29 v2 Spectral Theory

Authors: Carolyn S. Gordon , Craig J. Sutton

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Abstract

We show that within the class of left-invariant naturally reductive metrics $\mathcal{M}_{\operatorname{Nat}}(G)$ 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.

Keywords

naturally reductive metrics simple lie groups spectral isolation isospectral compact symmetric spaces left-invariant metrics spectrum

Cite

@article{arxiv.0707.0853,
  title  = {Spectral isolation of naturally reductive metrics on simple Lie groups},
  author = {Carolyn S. Gordon and Craig J. Sutton},
  journal= {arXiv preprint arXiv:0707.0853},
  year   = {2010}
}

Comments

19 pages, new title and abstract, revised introduction, new result demonstrating that any collection of isospectral compact symmetric spaces must be finite, to appear Math Z. (published online Dec. 2009)

Spectral isolation of naturally reductive metrics on simple Lie groups

Abstract

Keywords

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