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.
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C. S. Gordon’s research was partially supported by National Science Foundation grant DMS 0605247.
C. J. Sutton’s research was partially supported by an NSF Postdoctoral Fellowship and NSF Grant DMS 0605247.
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Gordon, C.S., Sutton, C.J. Spectral isolation of naturally reductive metrics on simple Lie groups. Math. Z. 266, 979–995 (2010). https://doi.org/10.1007/s00209-009-0640-6
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DOI: https://doi.org/10.1007/s00209-009-0640-6