Harmonic maps from Finsler manifolds. (English) Zbl 0996.53047

Summary: 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 \(\varphi\) from a Finsler manifold to a Riemannian manifold. We show that \(\varphi\) is an extremal of the energy functional if and only if \(\varphi\) 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.


53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
53C43 Differential geometric aspects of harmonic maps