Some Properties About The Canonical Hermitian Connections And Dirac Operators On Almost Kahler Manifolds

In my thesis, I mainly discuss the topics of almost Kahler manifolds, including the definition, the canonical hermitian connections on almost Kahler manifolds, and the corresponding Dirac operators of these connections. In particular, we firstly give the definition of symplectic manifolds, talking about their relation with almost complex structures and then give the definitions of canonical class of symplectic manifolds. We then state the definition of general almost Kahler manifolds, and their relation with symplectic manifolds. From the (m,n) decomposition of tangent vector value forms, we also describe the canonical hermitian connections and their several relations. Furthermore, we talk about their corresponding Dirac operators and then give a comparison between the several Dirac operators.