Isospectral pairs of metrics on balls, spheres, and other manifolds with different local geometries

Details Isospectral pairs of metrics on balls, spheres, and other manifolds with different local geometries Isospectral pairs of metrics on balls, spheres, and other manifolds with different local geometries

2000-11-05

arxiv.org/abs/math/0011033v1

Mathematics

Differential Geometry

43 pages. After retrieving source, read README file or type tex whole to typeset (in Unix)

Scientific paper

The first isospectral pairs of metrics are constructed on balls and spheres. This long standing problem, concerning the existence of such pairs, has been solved by a new method called "Anticommutator Technique." Among the wide range of such pairs, the most striking examples are provided on (4k-1)-dimensional spheres, where k > 2. One of these metrics is homogeneous (since it is the metric on the geodesic sphere of a 2-point homogeneous space), while the other is locally inhomogeneous. These examples demonstrate the surprising fact that no information about the isometries is encoded in the spectrum of Laplacian acting on functions. In other words, "The group of isometries, even the local homogeneity property, is lost to the "Non-Audible" in the debate of "Audible versus Non-Audible Geometry"."

Affiliated with

Also associated with

No associations

Rating

Isospectral pairs of metrics on balls, spheres, and other manifolds with different local geometries does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Isospectral pairs of metrics on balls, spheres, and other manifolds with different local geometries, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Isospectral pairs of metrics on balls, spheres, and other manifolds with different local geometries will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-241320