Conformal Invariants And The Wodzicki Residue For Complex Manifolds

For an even dimensional compact oriented conformal real manifold without boundary, Connes has constructed a canonical Fredholm module and defined a conformal invariant by the Wodzicki residue.In particular,in the 4-dimensional case,this invariant has been explicitly computed by the conformal deformation way.Ugalde has generalized Connes' result to the higher dimensional case and he has gave an explicit expression of the Connes' invariant in the flat case and indicated the way of computation in the general case.In this paper,for complex manifolds,we construct a conformal invariant using the Wodzicki residue and the(?) operator in the framework of Connes.We compute this conformal invariant in the flat case.