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

Carolyn S. Gordon^{[1]}; Dorothee Schueth^{[2]}; Craig J. Sutton^{[1]}

- [1] Dartmouth College Department of Mathematics Hanover, NH 03755 (USA)
- [2] Humboldt-Universität Institut für Mathematik Unter den Linden 6 10099, Berlin (Germany)

Annales de l’institut Fourier (2010)

- Volume: 60, Issue: 5, page 1617-1628
- ISSN: 0373-0956

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topGordon, Carolyn S., Schueth, Dorothee, and Sutton, Craig J.. "Spectral isolation of bi-invariant metrics on compact Lie groups." Annales de l’institut Fourier 60.5 (2010): 1617-1628. <http://eudml.org/doc/116316>.

@article{Gordon2010,

abstract = {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.},

affiliation = {Dartmouth College Department of Mathematics Hanover, NH 03755 (USA); Humboldt-Universität Institut für Mathematik Unter den Linden 6 10099, Berlin (Germany); Dartmouth College Department of Mathematics Hanover, NH 03755 (USA)},

author = {Gordon, Carolyn S., Schueth, Dorothee, Sutton, Craig J.},

journal = {Annales de l’institut Fourier},

keywords = {Laplacian; eigenvalue spectrum; Lie group; left-invariant metric; bi-invariant metric; bi-invariant metric.},

language = {eng},

number = {5},

pages = {1617-1628},

publisher = {Association des Annales de l’institut Fourier},

title = {Spectral isolation of bi-invariant metrics on compact Lie groups},

url = {http://eudml.org/doc/116316},

volume = {60},

year = {2010},

}

TY - JOUR

AU - Gordon, Carolyn S.

AU - Schueth, Dorothee

AU - Sutton, Craig J.

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

JO - Annales de l’institut Fourier

PY - 2010

PB - Association des Annales de l’institut Fourier

VL - 60

IS - 5

SP - 1617

EP - 1628

AB - 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.

LA - eng

KW - Laplacian; eigenvalue spectrum; Lie group; left-invariant metric; bi-invariant metric; bi-invariant metric.

UR - http://eudml.org/doc/116316

ER -

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