在复几何的研究中，调和映照的理论和应用起到了至关重要的作用。关于Kahler流形以及Hermite流形间各种调和映照已经有了大量的研究，取得了丰富的成果。而近Hermite流形间的调和映照的相关研究目前还很少，结果尚未成熟。本项目拟研究近Hermite流形间Hermite调和映照的相关问题。首先，我们拟研究近Hermite流形间Hermite调和映照热流的短时间存在性、长时间存在性和收敛性，从而建立Hermite调和映照的存在性。其次，我们拟研究近Hermite流形间Hermite多重调和映照与Hermite调和映照的全纯性。最后，我们拟在Bakry-Emery Ricci曲率条件下，建立近Hermite流形间Hermite调和映照的Schwarz引理。通过本项目的研究，将使我们对近Hermite流形有更加深入的认识和理解，也将进一步丰富调和映照的理论。

In the study of complex geometry, the theory and application of harmonic maps play an important role. Harmonic maps between Kahler manifolds and various harmonic maps from Hermitian manifolds have been widely and deeply studied by many geometers. However, there are few researches on the harmonic maps between almost Hermitian manifolds and the results are not yet mature. In this project, we intend to study the problems related to Hermitian harmonic maps between almost Hermitian manifolds. First of all, we will study the short-time existence, the long-time existence and the convergence of Hermitian harmonic maps heat flow between almost Hermitian manifolds to obtain the existence of Hermitian harmonic maps. Secondly, we will study the holomorphicity of Hermitian pluriharmonic maps and Hermitian harmonic maps between almost Hermitian manifolds. Finally, we will establish Schwarz lemmas for Hermitian harmonic maps between almost Hermitian manifolds under the Bakry-Emery Ricci curvature. Through the study of this project, we will have a better understanding of almost Hermitian manifolds. It will also further enrich the theory of harmonic maps.