[For part I see Commun. Partial Differ. Equations 12, 351-413 (1987; Zbl 0615.58033).]
Let be a compact complex -dimensional Hermitian manifold with smooth boundary M and let denote the -Laplacian on (p,q) forms on , which satisfy the -Neumann boundary conditions. In part I the asymptotic expansion of tr exp(-t as was obtained. In this part II the authors go on to show that the coefficients in the trace expansion are integrals of local geometric invariants. Suppose that at each point of M, is either strictly pseudoconvex or strictly pseudoconcave. Suppose also that is equipped with a Hermitian metric which is Kähler in a neighborhood of the boundary M and which induces a Levi metric on M. Then for
If is strictly pseudoconvex (pseudoconcave) then the expansion also holds for . The coefficients are integrals over of universal polynomials in the components of the curvature and torsion of the Hermitian connection and their covariant derivatives with respect to this connection. The coefficients and are integrals over M of universal polynomials in the components of the second fundamental form of M, the curvature and torsion of the Webster-C. M. Stanton connection, and their covariant derivatives with respect to this connection, as well as the components of the Hermitian curvature of and its Hermitian covariant derivatives on M.