5-7【Hongyu Wang】On D^+_J operator on higher dimensional almost Kahler manifolds

In this paper, we de ne D^+_J operator that is a generalized operator on higher dimensional almost Kahler manifolds. In terms of D^+_ J operator, we study-problem in almost Kahler geometry and the generalized Monge-Ampere equation on almost Kahler manifolds. Similarly to the Kahler case, we obtain  C^\infty a priori estimates for the solution of the generalized Monge-Ampere equation on the almost Kahler manifold (M,\omega, J) depended only on and J. Then as done in Kahler geometry, we study Calabi conjecture for almost Kahler manifolds. Finally, we will pose some questions in almost Kahler geometry.