Preprint 72/2007

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

Corey Dunn, Peter B. Gilkey, and JeongHyeong Park

Contact the author: Please use for correspondence this email.
Submission date: 08. Aug. 2007
Pages: 5
published in: Journal of physics / A, 41 (2008) 13, art-no. 135204 
DOI number (of the published article): 10.1088/1751-8113/41/13/135204
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
Download full preprint: PDF (117 kB), PS ziped (172 kB)

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.

23.06.2018, 02:11