Spectral isolation of naturally reductive metrics on simple Lie groups

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• 作者：Carolyn S. Gordon and Craig J. Sutton
• 关键词：Laplacian ; Eigenvalue spectrum ; Naturally reductive metrics ; Symmetric spaces
• 刊名：Mathematische Zeitschrift
• 出版年：2010
• 出版时间：December 2010
• 年：2010
• 卷：266
• 期：4
• 页码：979-995
• 全文大小：268.3 KB

文摘

We show that within the class of left-invariant naturally reductive metrics M_Nat(G){\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.