  In this paper, by using the Bochner technique on almost Hermitian manifolds,
we obtain a complex Hessian comparison for almost Hermitian manifolds
generalizing the Laplacian comparison for almost Hermitian manifolds by
Tossati, and reprove a diameter estimate for almost Hermitian manifolds by
Gray. Moreover, we obtain a sharp eigenvalue estimate on quasi Kaehler
manifolds and a sharp Hessian comparison on nearly Kaehler manifolds.
