Length spectrum invariants of Riemannian manifolds
type: Item
instance of: scholarly article
title: Length spectrum invariants of Riemannian manifolds
zbMATH Open document ID: 0804.53068
DOI: 10.1007/BF03025724
author: Georgi Popov
published in: Mathematische Zeitschrift
publication date: 1994-04-12T00:00:00Z
full work available at URL: https://eudml.org/doc/174532
review text: If \(X\) is a compact \(C^ \infty\)-smooth Riemannian manifold of dimension \(n\geq 2\), the length spectrum \({\mathcal L}(X)\) of \(X\) is defined as the set of lengths of all periodic geodesics in \(X\). The paper is concerned with new length spectrum invariants associated with closed elliptic geodesics. The invariants are given by the Liouville cohomology class of the KAM tori situated in a neighborhood of a closed elliptic geodesic. The author proves that the Liouville class of any of these tori is a spectral invariant of the Laplace-Beltrami operator for deformations of the Riemannian metric.
reviewed by: A. P. Stone
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 549774
zbMATH Keywords: length spectrum
zbMATH Keywords: periodic geodesics
zbMATH Keywords: closed elliptic geodesics
zbMATH Keywords: Liouville class
zbMATH Keywords: Laplace-Beltrami operator
Wikidata QID: Q115391011
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 549774