CUNY Graduate Center Differential Geometry Seminar presents

Isospectral Riemannian manifolds with different local geometry

Carolyn S. Gordon

Dartmouth College

Wednesday, September 12

2:30-3:30 pm, Room 4422

To what extent does the spectrum of the Laplacian of a compact Riemannian manifold determine its geometry? We will address this question by discussing a method for constructing isospectral manifolds with different local geometry. Examples will reveal various curvature properties which are not spectrally determined.

For non-compact manifolds, one considers the scattering poles instead of the spectrum (which need no longer be discrete). We construct continuous families of isoscattering metrics given by compact perturbations of the Euclidean metric on R^n.

Carolyn.S.Gordon@Dartmouth.edu