Spectral isolation of naturally reductive metrics on simple Lie groups

Details Spectral isolation of naturally reductive metrics on simple Lie groups Spectral isolation of naturally reductive metrics on simple Lie groups

2007-07-05

arxiv.org/abs/0707.0853v2

Mathematics

Differential Geometry

19 pages, new title and abstract, revised introduction, new result demonstrating that any collection of isospectral compact sy

Scientific paper

10.1007/s00209-009-0640-6

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.

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