关于多重调和映射与仿多重调和映射的位势之间的关系

到建筑的多重调和映射与对称微分

Pluriharmonic maps into buildings and symmetric differentials

本研究将Gromov-Schoen的多重调和映射构造推广到复光滑拟射影簇情形，构造了到Bruhat-Tits建筑的等变多重调和映射，并借此将Brunebarbe等人关于整体对数对称微分非零性的结论推广到拟射影情形。

On pseudoholomorphic map between almost Hermitian manifolds

In this paper, we use the canonical connection instead of Levi-Civita connection to study the smooth maps between almost Hermitian manifolds, especially, the pseudoholomorphic ones. By using the Bochner formulas, we obtian the $C^2$-estimate of canonical second fundamental form, Liouville type theorems of pseudoholomorphic maps, pseudoholomorphicity of pluriharmonic maps, and Simons integral inequality of pseudoholomorphic isometric immersion.

On $(H,\widetilde{H})$-harmonic Maps between pseudo-Hermitian manifolds

In this paper, we investigate critical maps of the horizontal energy functional $E_{H,\widetilde{H}}(f)$ for maps between two pseudo-Hermitian manifolds $(M^{2m+1},H(M),J,θ)$ and $(N^{2n+1},\widetilde{H}(N), \widetilde{J},\widetildeθ)$. These critical maps are referred to as $(H,\widetilde{H})$-harmonic maps. We derive a CR Bochner formula for the horizontal energy density $|df_{H, \widetilde{H}}|^{2}$, and introduce a Paneitz type operator acting on maps to refine the Bochner formula. As a result, we are able to establish some Bochner type theorems for $(H,\widetilde{H})$-harmonic maps. We al…

Harmonic maps and para-Sasakian geometry

The purpose of this paper is to study the harmonicity of maps to or from para-Sasakian manifolds. We derive the condition for the tension field of paraholomorphic map between almost para-Hermitian manifold and para-Sasakian manifold. The necessary and sufficient condition for a paraholomorphic map between para-Sasakian manifolds to be parapluriharmonic are shown and a non-trivial example is presented for its illustrations.