## Some properties of harmonic maps for Finsler manifolds.(English)Zbl 1135.53054

The paper studies properties of harmonic maps between Finsler manifolds. Several rigidity theorems for such maps are given. The stress-energy tensor for maps between Finsler manifolds is defined, and related integral formulas are obtained. As well, it is proved that any conformal strongly harmonic map from a Finsler manifold of dimension $$n>2$$ to a Finsler manifold must be homothetic.

### MSC:

 53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics) 53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics) 53C43 Differential geometric aspects of harmonic maps

### Keywords:

Finsler metric; harmonic map; conformal map; homothetic map.