Abstract
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 \(|df|^2< m-2\).
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Chiang, YJ. Exponentially harmonic maps between Finsler manifolds. manuscripta math. 157, 101–119 (2018). https://doi.org/10.1007/s00229-017-0981-0
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DOI: https://doi.org/10.1007/s00229-017-0981-0