Harmonic vector fields and the Hodge Laplacian operator on Finsler geometry

Concurrent vector fields on Finsler spaces

In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fields. We also prove that an L-reducible Finsler metric admitting a concurrent vector field reduces to a Landsberg metric.In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fi...

Characterization of Closed Vector Fields in Finsler Geometry

The π-exterior derivative d, which is the Finslerian generalization of the (usual) exterior derivative d of Riemannian geometry, is defined. The notion of a d-closed vector field is introduced and investigated. Various characterizations of d-closed vector fields are established. Some results concerning d-closed vector fields in relation to certain special Finsler spaces are obtained. 1

On the Parallel Displacement and Parallel Vector Fields in Finsler Geometry

In Finsler geometry, the notion of parallel for Finsler tensor fields is defined, already. In this paper, however, for vector fields on a base manifold, the author studies the notion of parallel. In the last section, the obtained results are shown as compare corresponding properties to them of Riemannian geometry. Introduction The author gave the definition (1.1) of the parallel displacement al...

Finsler Geometry of Projectivized Vector Bundles

Harmonic-killing Vector Fields *

In this paper we consider the harmonicity of the 1-parameter group of local infinitesimal transformations associated to a vector field on a (pseudo-) Riemannian manifold to study this class of vector fields, which we call harmonic-Killing vector fields.