Related papers: Killing Correspondence in Finsler Spaces
The Killing equation for a general Finsler space is set up. It is showed that the Killing equation of $(\alpha,\beta)$ space can be divided into two parts. One is the same with Killing equation of a Riemannian metric, another equation can…
The correspondence between wind Riemannian structures and spacetimes endowed with a Killing vector field is deepened by considering a cone structure endowed with a vector field that preserve the structure (termed "cone Killing vector…
We study Finsler spacetimes and Killing vector fields taking care of the fact that the generalized metric tensor associated to the Lorentz-Finsler function $L$ is in general well defined only on a subset of the slit tangent bundle. We then…
Recently we have obtained the Cartan connection for the Finsler space whose metric is given by an exponential change with an h-vector. In this paper, we discuss certain geometric properties of a Finslerian hyperspace subjected to an…
We study space-time Killing vectors in terms of their "lapse and shift" relative to some spacelike slice. We give a necessary and sufficient condition in order for these lapse-shift pairs, which we call Killing initial data (KID'S), to form…
In this paper, we investigate the change of Finslr metrics $$L(x,y) \to\bar{L}(x,y) = f(e^{\sigma(x)}L(x,y),\beta(x,y)),$$ which we refer to as a generalized $\beta$-conformal change. Under this change, we study some special Finsler spaces,…
In this paper, we introduce and investigate a general transformation or change of Finsler metrics, which is referred to as a generalized $\beta$-conformal change: $$L(x,y) \longrightarrow\overline{L}(x,y) =…
On a Finsler manifold $(M,L)$, we consider the change $L\longrightarrow\bar{L}(x,y)=e^{\sigma(x)}L(x,y)+\beta (x,y)$, which we call a $\beta$-conformal change. This change generalizes various types of changes in Finsler geometry: conformal,…
The study of curvature properties of homogeneous Finsler spaces with $(\alpha, \beta)$-metrics is one of the central problems in Riemann-Finsler geometry. In the present paper, the existence of invariant vector fields on homogeneous Finsler…
In this paper, we study Clifford-Wolf translations of Finsler spaces. We first give a characterization of Clifford-Wolf translations of Finsler spaces in terms of Killing vector fields. In particular, we show that there is a natural…
In this paper, first we prove the existence of invariant vector field on a homogeneous Finsler space with infinite series $(\alpha, \beta)$-metric and exponential metric. Next, we deduce an explicit formula for the the $S$-curvature of…
For the general class of pseudo-Finsler spaces with $(\alpha,\beta)$-metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means that the fundamental tensor has Lorentzian…
In this paper, the Killing vector will be constructed for the $R$-spacetime metric. The symmetry transformations corresponding to this vectors are obtained explicitly. Their coincidence with the transformations of the Poincar\'e group in a…
In this paper, we first deduce a formula of S-curvature of homogeneous Finsler spaces in terms of Killing vector fields. Then we prove that a homogeneous Finsler space has isotropic S-curvature if and only if it has vanishing S-curvature.…
Some basic theorems on Killing vector fields are reviewed. In particular, the topic of a constant-curvature space is examined. A detailed proof is given for a theorem describing the most general form of the metric of a homogeneous isotropic…
The present paper deals with an \emph{intrinsic} investigation of the notion of a concurrent $\pi$-vector field on the pullback bundle of a Finsler manifold $(M,L)$. The effect of the existence of a concurrent $\pi$-vector field on some…
We investigate what we call a conformal $\beta $ - change in Finsler spaces, namely $$ L(x,y)\to ~^{\ast}L(x,y)=e^{\sigma(x)}L(x,y)+\beta(x,y)$$ where~$\sigma ~$ is a function of $x~ only ~and ~ \beta (x, y)$ is a given 1- form. This change…
Recently, we have studied the Finsler space with h-Matsumoto change and found Cartan connection for the transformed space [2]. In this paper, we have discussed certain geometrical properties of the hypersurface of a Finsler space for the…
Killing vector fields of constant length correspond to isometries of constant displacement. Those in turn have been used to study homogeneity of Riemannian and Finsler quotient manifolds. Almost all of that work has been done for group…
In the present paper, the notion of $\mathbb{R}$-complex Finsler space with Infinite Series ($\alpha, \beta$)- metric $\dfrac{\beta^2}{\beta - \alpha}$ is defined. The Fundamental metric fields $g_{ij}$, $g_{i\bar{j}}$, their determinants…