The spectral geometry of Riemannian submersions
John Leahy
(University of Oregon)
Saturday, November 9, 1996
11:30 AM
We study the spectral geometry of a Riemannian submersion p: Z ->
Y. We give necessary and sufficient conditions for
p* to preserve the eigenforms of the Laplacian. We show
that if the pull-back of an eigenform is an eigenform, then the
eigenvalue can only increase. If G is a compact, connected Lie
group with H1(G;R ) not equal to 0, we give examples of
principal G-bundles over homogeneous manifolds where the
pull-back of an eigenform from the base is an eigenform on the total
space with a different eigenvalue.
Back to
Fall 1996 meeting of the PNGS.
Suggestions or corrections to
Jack Lee <lee@math.washington.edu>.