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Spectral geometry, homogeneous spaces, and differential forms with finite Fourier series
Corey Dunn, Peter B. Gilkey and JeongHyeong ParkAbstract
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.
- Received:
- 08.08.07
- Published:
- 08.08.07
- MSC Codes:
- 58J50
- PACS:
- 02.20.Qs, 02.30.Em, 02.30.Nw, 02.40.Vh
- Keywords:
- eigenform, Finite Fourier Series, Laplace-Beltrami, Peter Weyl theorem, Laplace-Beltrami Operator