We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
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.