Conformal $\mathcal {F}$-harmonic maps for Finsler manifolds
Volume 134 / 2014
Colloquium Mathematicum 134 (2014), 227-234
MSC: 53C60, 58E20, 53B40.
DOI: 10.4064/cm134-2-6
Abstract
By introducing the ${\mathcal F}$-stress energy tensor of maps from an $n$-dimensional Finsler manifold to a Finsler manifold and assuming that $(n-2){\mathcal F(t)}'-2t{\mathcal F(t)}''\not =0$ for any $t\in [0, \infty )$, we prove that any conformal strongly ${\mathcal F}$-harmonic map must be homothetic. This assertion generalizes the results by He and Shen for harmonics map and by Ara for the Riemannian case.
