Isospectral manifolds with different local geometries
Abstract
We construct several new classes of isospectral manifolds with different local geometries. After reviewing a theorem by Carolyn Gordon on isospectral torus bundles and presenting certain useful specialized versions (Chapter 1) we apply these tools to construct the first examples of isospectral fourdimensional manifolds which are not locally isometric (Chapter 2). Moreover, we construct the first examples of isospectral left invariant metrics on compact Lie groups (Chapter 3). Thereby we also obtain the first continuous isospectral families of globally homogeneous manifolds and the first examples of isospectral manifolds which are simply connected and irreducible. Finally, we construct the first pairs of isospectral manifolds which are conformally equivalent and not locally isometric (Chapter 4).
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2001
 arXiv:
 arXiv:math/0102123
 Bibcode:
 2001math......2123S
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Spectral Theory;
 58J53
 EPrint:
 59 pages, AMSTeX. Habilitation thesis (2000), to appear in: J. Reine Angew. Math