  We prove that if an (n-1)-dimensional torus acts symplectically on a
2n-dimensional manifold, then the action has a fixed point if and only if the
action is Hamiltonian. One may regard it as a symplectic version of Frankel
theorem. The case of n=2 is the well known theorem of McDuff. From the well
known example of McDuff (a six dimensional symplectic non-Hamiltonian circle
action with fixed tori) and its products with copies of a two dimensional
sphere with the usual rotation, the condition on the dimension of the acting
torus is optimal to obtain the result.
