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Spectral isolation of bi-invariant metrics on compact Lie groups

Carolyn S. Gordon, Dorothee Schueth, Craig J. Sutton (2010)

Annales de l’institut Fourier

We show that a bi-invariant metric on a compact connected Lie group G is spectrally isolated within the class of left-invariant metrics. In fact, we prove that given a bi-invariant metric g 0 on G there is a positive integer N such that, within a neighborhood of g 0 in the class of left-invariant metrics of at most the same volume, g 0 is uniquely determined by the first N distinct non-zero eigenvalues of its Laplacian (ignoring multiplicities). In the case where G is simple, N can be chosen to be two....

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