Spectral geometry, homogeneous spaces, and differential forms with finite Fourier series

Corey Dunn, Peter B. Gilkey, and JeongHyeong Park
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Submission date: 08. Aug. 2007
Pages: 5
MSC-Numbers: 58J50
PACS-Numbers: 02.20.Qs, 02.30.Em, 02.30.Nw, 02.40.Vh
Keywords and phrases: eigenform, Finite Fourier Series, Laplace-Beltrami, Peter Weyl theorem, Laplace-Beltrami Operator
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Abstract:
Let G be a compact Lie group acting transitively on Riemannian manifolds M and N and let p be an equivariant Riemannian submersion from M to N. We show that a smooth differential form on N has finite Fourier series on N if and only if the pull-back has finite Fourier series on M.