Local Riemann-Roch theorem for almost Hermitian manifolds

Abstract

In this paper, we give a local Riemann-Roch theorem for certain almost Hermitian manifolds by a canonical connection and the theory of almost Hermitian structure of null eccentricity. In particular, we obtain a local Riemann-Roch theorem for all closed almost complex manifolds of dimension 4. Also, by using the heat equation method, we give an analytic approach to a local index theorem for generalized Dirac operators.