Mathematical Research Letters

Volume 21 (2014)

Number 4

Hermitian harmonic maps and non-degenerate curvatures

Pages: 831 – 862



Kefeng Liu (Department of Mathematics, University of California at Los Angeles)

Xiaokui Yang (Department of Mathematics, Northwestern University, Evanston, Illinois, U.S.A.)


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].

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