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- Title
Spectral isolation of naturally reductive metrics on simple Lie groups.
- Authors
Gordon, Carolyn; Sutton, Craig
- Abstract
We show that within the class of left-invariant naturally reductive metrics $${\mathcal{M}_{{\rm Nat}}(G)}$$ 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.
- Subjects
SPECTRAL theory; LIE groups; INVARIANTS (Mathematics); METRIC spaces; SYMMETRIC spaces; EIGENVALUES; MATHEMATICAL analysis
- Publication
Mathematische Zeitschrift, 2010, Vol 266, Issue 4, p979
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-009-0640-6