Length and eigenvalue equivalence
几何拓扑
2008-04-01 v2 群论
摘要
Two Riemannian manifolds are called eigenvalue equivalent when their sets of eigenvalues of the Laplace-Beltrami operator are equal (ignoring multiplicities). They are (primitive) length equivalent when the sets of lengths of their (primitive) closed geodesics are equal. We give a general construction of eigenvalue equivalent and primitive length equivalent Riemannian manifolds. For example we show that every finite volume hyperbolic --manifold has pairs of eigenvalue equivalent finite covers of arbitrarily large volume ratio. We also show the analogous result for primitive length equivalence.
引用
@article{arxiv.math/0606343,
title = {Length and eigenvalue equivalence},
author = {Christopher J. Leininger and D. B. McReynolds and Walter D. Neumann and Alan W. Reid},
journal= {arXiv preprint arXiv:math/0606343},
year = {2008}
}