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Harmonic vector fields on a weighted Riemannian manifold arising from a Finsler structure

Authors
  • Shojaee, Neda
  • Rezaii, Morteza Mirmohammad
Type
Published Article
Journal
Advances in Pure and Applied Mathematics
Publisher
De Gruyter
Publication Date
Sep 23, 2017
Volume
9
Issue
2
Pages
131–141
Identifiers
DOI: 10.1515/apam-2016-0099
Source
De Gruyter
Keywords
License
Yellow

Abstract

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.

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