## 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.

### MSC:

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