O Isospectral Deformations on TwoStep Nilmanifolds
Abstract
Two Riemannian manifolds are said to be isospectral if the associated Laplace operators have the same spectrum. C. Gordon and E. Wilson constructed isospectral deformations of leftinvariant metrics on nilmanifolds. Chapter One of the thesis proves that for twostep nilmanifolds, the only isospectral deformations are the ones contructed by Gordon and Wilson. In Chapter Two, I reprove the GordonWilson isospectral deformation theorem on twostep nilmanifolds from a point of view of analysis on line bundles. Given a line bundle over a nilmanifold together with a Riemannian metric on the base nilmanifold and a connection on the bundle, one obtains a Laplace operator acting on the sections of the line bundle. In Chapter Three, I investigate how the spectrum of this Laplace operator changes as the metric and connection are deformed. Several examples are studied.
 Publication:

Ph.D. Thesis
 Pub Date:
 1991
 Bibcode:
 1991PhDT........35O
 Keywords:

 NILMANIFOLDS;
 Mathematics; Physics: General