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Spectral geometry, homogeneous spaces, and differential forms with finite Fourier series
Corey Dunn, Peter B. Gilkey and JeongHyeong Park
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.