The Weinstein Conjecture in Product of Symplectic Manifolds

TL;DR

This paper proves the Weinstein conjecture for certain products of symplectic manifolds using pseudo-holomorphic curves, extending the conjecture's validity to new classes of manifolds.

Contribution

It establishes the Weinstein conjecture in the product of two strongly geometrically bounded symplectic manifolds under specific conditions, including cases involving complex projective spaces and cotangent bundles.

Findings

Weinstein conjecture holds in products of certain symplectic manifolds.

Results apply to manifolds like P^2 imes T^*N.

Method involves pseudo-holomorphic curve techniques.

Abstract

In this paper, using pseudo-holomorphic curve method, one proves the Weinstein conjecture in the product $P_1\times P_2$ of two strongly geometrically bounded symplectic manifolds under some conditions with $P_1$. In particular, if $N$ is a closed manifold or a noncompact manifold of finite topological type, our result implies that the Weinstein conjecture in $\mathbb{C}\mathbb{P}^2\times T^*N$ holds.