Periodic Reeb orbits on prequantization bundles

Abstract

In this paper, we prove that every graphical hypersurface in a prequantization bundle over a symplectic manifold $M$, pinched between two circle bundles whose ratio of radii is less than $\sqrt{2}$ carries either one short simple periodic orbit or carries at least $\mathrm{cuplength}(M)+1$ simple periodic Reeb orbits.

25 pages, 3 figures. Several arguments have been cleaned up and clarified

References in corpus (2)

• Polyfold and Fredholm Theory I: Basic Theory in M-Polyfolds
• On the minimal number of periodic orbits on some hypersurfaces in ${\mathbb{R}}^{2n}$

Cited by in corpus (2)

• Symplectic Homology of complements of smooth divisors
• A Boothby-Wang theorem for Besse contact manifolds