Two remarks on the length spectrum of a Riemannian manifold-Reference-Cited by-同舟云学术

Two remarks on the length spectrum of a Riemannian manifold

Published:2011-03-25 Issue:11 Volume:139 Page:4113-4119
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Schmidt Benjamin,Sutton Craig

Abstract

We demonstrate that every closed manifold of dimension at least two admits smooth metrics with respect to which the length spectrum is not a discrete subset of the real line. In contrast, we show that the length spectrum of any real analytic metric on a closed manifold is a discrete subset of the real line. In particular, the length spectrum of any closed locally homogeneous space forms a discrete set.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2011-139-11/S0002-9939-2011-10815-3/S0002-9939-2011-10815-3.pdf

Reference12 articles.

1. Bumpy metrics;Abraham, R.,1970

2. Generic properties of closed geodesics;Anosov, D. V.;Izv. Akad. Nauk SSSR Ser. Mat.,1982

3. Formule de Poisson pour les variétés riemanniennes;Chazarain, J.;Invent. Math.,1974

4. [DGS] B. De Smit, R. Gornet and C. J. Sutton, Sunada’s method and the covering spectrum, J. Differential Geom. 86 (2010), no. 3, 501–537.

5. The spectrum of positive elliptic operators and periodic bicharacteristics;Duistermaat, J. J.;Invent. Math.,1975

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