The First Eigenvalue of a Homogeneous CROSS
The First Eigenvalue of a Homogeneous CROSS
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DOI：
10.1007/s12220-021-00826-7
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发表时间：
2020-01
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影响因子：
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通讯作者：
R. G. Bettiol;E. Lauret;P. Piccione
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文献类型：
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作者：
R. G. Bettiol;E. Lauret;P. Piccione
本文给出了具有齐次度量的紧致秩一对称空间（CROSS）上Laplace-Beltrami算子的第一特征值的显式表达式。作为后果，我们证明了均匀度量的CROSSes等谱当且仅当他们是等距的，并讨论了他们的稳定性（或缺乏）作为解决方案的Yamabe问题。
We provide explicit formulae for the first eigenvalue of the Laplace–Beltrami operator on a compact rank one symmetric space (CROSS) endowed with any homogeneous metric. As consequences, we prove that homogeneous metrics on CROSSes are isospectral if and only if they are isometric, and also discuss their stability (or lack thereof) as solutions to the Yamabe problem.