Carolyn Gordon, Dartmouth College

Spectral Geometry on Line Bundles over Flat Tori

Let M be a closed Riemannian manifold and L a Hermitian line bundle over M. Each Hermitian connection on L gives rise to a Laplace operator acting on sections of L. We consider the question: How much information about the connection or the curvature of the connection is encoded in the spectrum of the Laplace operator? We also consider the analogous questions for Schrödinger operators on line bundles. We will focus primarily on the setting of line bundles over flat tori.

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