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In the present work, the harmonic vector field is defined on closed Finsler measure spaces through different approaches. At first, the weighted harmonic vector field is obtained as the solution space of a PDE system. Then a suitable Dirichlet energy functional is introduced. A σ-harmonic vector field is considered as the critical point of related action. It is proved that a σ-harmonic vector field on a closed Finsler space with an extra unit norm condition is an eigenvector of the defined Laplacian operator on vector fields. Moreover, we prove that a unit weighted harmonic vector field on a closed generalized Einstein manifold is a σ-harmonic vector field. [ABSTRACT FROM AUTHOR]

In this paper, some properties of F-harmonic and conformal F-harmonic maps between doubly warped product manifolds are studied and new examples of non-harmonic F-harmonic maps are constructed. [ABSTRACT FROM AUTHOR]