What is it about?
In this paper, authors try to define harmonic vector fields on Finsler manifolds no nead to lift vector fields on tangent bundle.
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Why is it important?
Different lifts of vector fields, give us different equations to define harmonic vector fields i.e, the concept of harmonic vector fields depends on different kind of lifting, and we solve this problem in this paper. On the other hand, we define harmonic vector fields as critical points of a suitable action. This new pde is too similar to Riemann case but is a nonlinear equation.
Perspectives
We hope other authors use these definitions to find some topological and geometric properties of Finsler manifolds.
Neda Shojaee
Amirkabir University of Technology
Read the Original
This page is a summary of: Harmonic vector fields on a weighted Riemannian manifold arising from a Finsler structure, Advances in Pure and Applied Mathematics, January 2017, De Gruyter,
DOI: 10.1515/apam-2016-0099.
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