Abstract
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 n-manifold has pairs of eigenvalue equivalent finite covers of arbitrarily large volume ratio.We also show the analogous result for primitive length equivalence.
Original language | English (US) |
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Article number | rnm135 |
Journal | International Mathematics Research Notices |
Volume | 2007 |
DOIs | |
State | Published - 2007 |
ASJC Scopus subject areas
- General Mathematics