Spectral isolation of naturally reductive metrics on simple Lie groups

Abstract

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

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)

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