## Illinois Journal of Mathematics

### Harmonic maps from Finsler manifolds

Xiaohuan Mo

#### Abstract

A Finsler manifold is a Riemannian manifold without the quadratic restriction. In this paper we introduce the energy functional, the Euler-Lagrange operator, and the stress-energy tensor for a smooth map $\phi$ from a Finsler manifold to a Riemannian manifold. We show that $\phi$ is an extremal of the energy functional if and only if $\phi$ satisfies the corresponding Euler-Lagrange equation. We also characterize weak Landsberg manifolds in terms of harmonicity and horizontal conservativity. Using the representation of a tension field in terms of geodesic coefficients, we construct new examples of harmonic maps from Berwald manifolds which are neither Riemannian nor Minkowskian.

#### Article information

Source
Illinois J. Math., Volume 45, Number 4 (2001), 1331-1345.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138069

Digital Object Identifier
doi:10.1215/ijm/1258138069

Mathematical Reviews number (MathSciNet)
MR1895460

Zentralblatt MATH identifier
0996.53047

#### Citation

Mo, Xiaohuan. Harmonic maps from Finsler manifolds. Illinois J. Math. 45 (2001), no. 4, 1331--1345. doi:10.1215/ijm/1258138069. https://projecteuclid.org/euclid.ijm/1258138069