Symplectic Toric Manifold And Its Extremal Metric

In this thesis we mainly consider symplectic toric manifolds and their extremal metrics.According to Delzant theorem we consider the method of how to construct a symplectic toric manifold,and we discuss the necessary and sufficient conditions for the existence of extremal metrics on the symplectic toric manifolds.Finally we compute several non-trivial examples about the theory mentioned above.