On Euler number of symplectic hyperbolic manifold.

In this article, we introduce a class of closed almost K\"{a}hler manifold $X^{2n}$ which called the special symplectic hyperbolic manifold. Those manifolds include K\"{a}hler hyperbolic manifolds. We show that the Euler number of a special symplectic manifold satisfies the inequality $(-1)^{n}\chi(X)>0$.