Isospectral Lie groups and isospectral spheres
by
Dorothee Schueth
University of Bonn

To which extent does the Laplace spectrum of a compact Riemannian manifold determine its geometry? In order to detect local geometric properties which are not spectrally determined one needs examples of isospectral manifolds which are not locally isometric. The main method used so far for constructing such manifolds involves certain torus actions. We give a useful reformulation in terms of connection forms and apply this to construct the first examples of left invariant isospectral metrics on compact Lie groups. A local property in which these isospectral metrics differ from each other is the norm of the Ricci tensor. Another application of the above method in its most recent form is the construction of isospectral spheres, first discovered by Carolyn Gordon in dimension at least eight. We shortly present some new examples of isospectral spheres in dimension five.

http://www.math.uni-bonn.de/people/schueth

Date received: March 27, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafv-89.