Topology and closed characteristics of \(K\)-contact manifolds
It is proved that the characteristic flow of a \(K\)-contact form has at least \(n + 1\) closed leaves on a \(2n + 1\)-dimensional manifold. The proof is obtained by applying the Ljusternik-Schnirelmann critical point theory to a suitable function. Moreover, by using Morse theory, it is proved that the first Betti number of a closed Sasakian manifold with finitely many closed characteristics is 0.
Ljusternik-Schnirelmann critical point theory
scientific article; zbMATH DE number 817251