n 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 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 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 fields. We also prove that an L-reducible Finsler metric admitting a Concurrent vector field reduces to a Landsberg metric.

‎Ricci bi-conformal vector fields have find their place in geometry as well as in physical applications‎. ‎In this paper‎, ‎we consider the Siklos spacetimes and we determine all the Ricci bi-conformal vector fields on these spaces‎.

Let M be an n-dimensional Riemannian manifold and TM its tangent bundle. The conformal and fiber preserving vector fields on TM have well-known physical interpretations and have been studied by physicists and geometricians. Here we define a Riemannian or pseudo-Riemannian lift metric ḡ on TM , which is in some senses more general than other lift metrics previously defined on TM , and seems to complete these works. Next we study the lift conformal vector fields ds on (TM, ḡ) and prove among the others that, every complete lift conformal vector field on TM is homothetic, and moreover, every horizontal or vertical lift conformal vector field on TM is a Killing vector.

We consider four-dimensional Lie groups equipped with left-invariant Einstein Lorentzian metrics. The harmonicity properties of left-invariant vector fields on these spaces are determined. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. Left-invariant vector fields defining harmonic maps are also classified, and the energy of these vector fields is explicitly calculated.

On a Finsler manifold, we define conformal vector fields and their complete lifts and prove that in certain conditions they are homothetic.

In this paper, we study N(k)-contact metric manifolds en-dowed with a torse-forming vector , field and give some characterizations for such manifolds. Then, we deal with N(k)-contact metric manifolds admitting a Ricci soliton and , nd that the potential vector , field V of the Ricci soliton is a constant multiple of ξ, . Also, we obtain a necessary condition for a torse-forming vector , field to be recurrent and Killing on M.