Spectral isolation of bi-invariant metrics on compact Lie groups

Details Spectral isolation of bi-invariant metrics on compact Lie groups Spectral isolation of bi-invariant metrics on compact Lie groups

2007-10-15

arxiv.org/abs/0710.2911v3

Ann. Inst. Fourier 60 (2010), no. 5, 1617-1628

Mathematics

Differential Geometry

10 pages, new title, revised abstract and introduction, minor typos corrected, to appear in Ann. Inst. Fourier (Grenoble)

Scientific paper

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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