Harmonic vector fields on a weighted Riemannian manifold arising from a Finsler structure
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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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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Transitivities of maps on G-spaces
- Lp-L2 estimates for solutions of the wave equation associated to the Grushin operator
- Gabor orthonormal bases generated by indicator functions of parallelepiped-shaped sets
- Riesz potentials of Radon measures associated to reflection groups
- Harmonic vector fields on a weighted Riemannian manifold arising from a Finsler structure
- An efficient method to compute the Moore–Penrose inverse
- The Thirring model in spaces of analytic functions
Artikel in diesem Heft
- Frontmatter
- Transitivities of maps on G-spaces
- Lp-L2 estimates for solutions of the wave equation associated to the Grushin operator
- Gabor orthonormal bases generated by indicator functions of parallelepiped-shaped sets
- Riesz potentials of Radon measures associated to reflection groups
- Harmonic vector fields on a weighted Riemannian manifold arising from a Finsler structure
- An efficient method to compute the Moore–Penrose inverse
- The Thirring model in spaces of analytic functions
