Harmonic maps from complex Finsler manifolds

Jingwei Han and Yibing Shen

Vol. 236 (2008), No. 2, 341–356

DOI: 10.2140/pjm.2008.236.341

Abstract

We derive the variation formula of the ∂-energy and of the ∂-energy for a smooth map from a complex Finsler manifold to an Hermitian manifold. Applying the result on a nonlinear elliptic system due to J. Jost and S. T. Yau, we obtain some existence theorems of harmonic maps from strongly Kähler Finsler manifolds to Kähler manifolds. Also, for such maps, we show that the difference between ∂-energy and ∂-energy is a homotopy invariant.

Keywords

complex Finsler metric, harmonic map, Kähler manifold, ∂-energy

Mathematical Subject Classification 2000

Primary: 53C60, 53B40

Milestones

Received: 8 November 2007

Accepted: 27 February 2008

Published: 1 June 2008