Harmonic maps of Finsler manifolds. (English) Zbl 1157.53032

Mihai, Adela (ed.) et al., Topics in differential geometry. Bucharest: Editura Academiei Române (ISBN 978-973-27-1656-4/hbk). 207-247 (2008).
The author provides a detailed presentation of the subject of harmonic maps between Finsler manifolds. With a brief review of harmonic maps of Riemannian manifolds the question is discussed how one can define energy functionals for maps between real or complex Finsler manifolds. The equations of harmonic maps are derived from the first variation formulas, and the second variation is studied. A concise overview on real and complex Finsler geometry is included as well. The last section is devoted to the regularity of weakly harmonic maps, and describes the means to obtain a (partial) regularity for energy minimizing weakly harmonic maps from a Riemannian into a Finsler manifold.
For the entire collection see [Zbl 1144.53005].


53C43 Differential geometric aspects of harmonic maps
53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
53C55 Global differential geometry of Hermitian and Kählerian manifolds