Exponentially harmonic maps between Finsler manifolds



Exponentially harmonic maps and harmonic maps are different. In this paper, we derive the first and second variations of the exponential energy of a smooth map between Finsler manifolds. We show that a non-constant exponentially harmonic map f from a unit m-sphere \(S^m\) (\(m\ge 3\)) into a Finsler manifold is stable in case \(|df|^2\ge m- 2\), and is unstable in case \(|df|^2< m-2\).

Mathematics Subject Classification

58E20 53C60 53B40 58B20 


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© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Mary WashingtonFredericksburgUSA

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