Harmonic maps from $\mathbb{C}^{n}$ to Kähler manifolds

Jianming Wan

Vol. 275 (2015), No. 1, 183–189

DOI: 10.2140/pjm.2015.275.183

Abstract

We prove that a harmonic map from ${ℂ}^n$ ($n\ge 2$) to any Kähler manifold must be holomorphic under an assumption on energy density. This can be considered as a complex analogue of the Liouville-type theorem for harmonic maps obtained by Sealey.

Keywords

harmonic maps, holomorphic maps

Mathematical Subject Classification 2010

Primary: 53C55

Milestones

Received: 6 May 2014

Revised: 31 August 2014

Accepted: 11 September 2014

Published: 12 April 2015