Harmonic maps from Finsler manifolds. (English) Zbl 0996.53047

Mo, Xiaohuan

Ill. J. Math. 45, No. 4, 1331-1345 (2001).

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

Keywords:

energy functional; Euler-Lagrange operator; stress-energy tensor; weak Landsberg manifolds; Berwald manifolds