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.
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