Illinois Journal of Mathematics

Harmonic maps from Finsler manifolds

Xiaohuan Mo

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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

Subjects
Primary: 53C43: Differential geometric aspects of harmonic maps [See also 58E20]
Secondary: 53C60: Finsler spaces and generalizations (areal metrics) [See also 58B20] 58E20: Harmonic maps [See also 53C43], etc.

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


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