‎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.

On a Finsler manifold, we define CONFORMAL VECTOR FIELDS and their complete lifts and prove that in certain conditions they are homothetic.

The navigation technique is very e, ective to obtain or classify a Finsler metric from a given a Finsler metric (especially a Riemannian metric) under an action of a VECTOR , eld on a di, erential manifold. In this survey, we will survey some recent progress on the navigation problem and CONFORMAL VECTOR , elds on Finsler manifolds, and their applications in the classi, cations of some Finsler metrics of scalar (resp. constant) ag curvature.

The target of this paper is to study N(k)-contact metric manifolds with some types of CONFORMAL VECTOR , elds like ,-holomorphic planar CONFORMAL VECTOR , elds and Ricci biCONFORMAL VECTOR , elds. We also characterize N(k)-contact metric manifolds allowing CONFORMAL Ricci almost soliton. Obtained results are supported by examples.

Modular invarinat, constraints the spectrum of the theory. Using the medum temprature expansion, for first and third order of derivative, a universal upper bound on the lowest primary field has been obtained in recent researches. In this paper, we will improve the upper bound, on the scaling dimension of the lowest primary field. We use by the medium temprature expansion for an arbitrary order of derivatives. We show that the upper bound depends on the order of derivative. In this research, we obtain the optimal values of the order of derivatives which leads to the best upper bound.

The Randers metrics are popular metrics similar to the Riemannian metrics, frequently used in physical and geometric studies. The weak Einstein-Finsler metrics are a natural generalization of the Einstein-Finsler metrics. Our proof shows that if $(M,F)$ is a simply-connected and compact Randers manifold and $F$ is a weak Einstein-Douglas metric, then every special projective VECTOR field is Killing on $(M,F)$. Furthermore, we demonstrate that if a connected and compact manifold $M$ of dimension $n \geq 3$ admits a weak Einstein-Randers metric with Zermelo navigation data $(h,W)$, then either the $S$-curvature of $(M,F)$ vanishes, or $(M,h)$ is isometric to a Euclidean sphere ${\mathbb{S}^n}(\sqrt{k})$, with a radius of $1/\sqrt{k}$, for some positive integer $k$.

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.