For a compact homogeneous space G / K, we study the problem of existence of G-invariant Riemannian metrics such that each eigenspace of the Laplacian is a real irreducible representation of G. We prove that the normal metric of a compact irreducible symmetric space has this property only in rank one. Furthermore, we provide existence results for such metrics on certain isotropy reducible spaces.
Mathematische Zeitschrift – Springer Journals
Published: May 31, 2018
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