Mathematical Research Letters
Volume 21 (2014)
Hermitian harmonic maps and non-degenerate curvatures
Pages: 831 – 862
In this paper, we study the existence of various harmonic maps from Hermitian manifolds to Kähler, Hermitian and Riemannian manifolds, respectively. Using refined Bochner formulas on Hermitian (possibly non-Kähler) manifolds, we derive new rigidity results on Hermitian harmonic maps from compact Hermitian manifolds to Riemannian manifolds, and we also obtain the complex analyticity of pluri-harmonic maps from compact complex manifolds to compact Kähler manifolds (and Riemannian manifolds) with nondegenerate curvatures, which are analogous to several fundamental results in [14, 26, 28].