Hamiltonian actions are studied. We prove that a symplectic (n-1)-dimensional torus action on a 2n-dimensional manifold has a fixed point if and only if the action is Hamiltonian. The result can be regarded as a symplectic version of the beautiful theorem by Frankel which says that Kahler circle action has a fixed point if and only if the action is Hamiltonian. Also, we construct an eight-dimensional compact symplectic non-Kahler manifold with a Hamiltonian circle action which has an isolated fixed point.
