Length spectrum invariants of Riemannian manifolds
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.
scientific article; zbMATH DE number 549774
scientific article