Double Conformal Invariants And The Wodzicki Residue

For General manifold, within the framework of Connes, we construct a new double conformal invariant using the Wodzicki residue. We compute this conformal invariant in the two-dimensional case. In addition to the complex manifold, we construct double conformal invariants using the same method, and calculate its two-dimensional case results.In the 0-order pseudodifferential operator S acting on rank r vector bundle B of the compact manifold M without boundary, and n-order dif-ferential formΩn on the C∞(M)×C∞(M).For n-order differential formΩn, we use the Wodzicki 1-density type form Wres([S, f][S,h]), for any f0,f, h∈C∞(M), where∫M f0Ωn(f, h) define the Hochschild 2-upper closed chain.In the calculation process, we take special circumstances, let (B, S) = (H, F), where f is the article [1] Connes mentioned in connection with the even-dimeionsnal compact conformal manifold without border-related F-mode, we transform the double conformal invariant. Refer to the article[14],[15] W.J.Ugalde method of calculation, we construct double conformal invariants calculation of calculation method, and calculate its two-dimensional case re-sults.