The Weinstein Conjecture in Product of Symplectic Manifolds

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 $\mathbb{C}{\mathbb{P}}^2\times T^{\ast }N$ holds.