Related papers: Special anisotropic conformal changes of conic pse…
The present work is devoted to investigate anisotropic conformal transformation of conic pseudo-Finsler surfaces $(M,F)$, that is, $ F(x,y)\longmapsto \overline{F}(x,y)=e^{\phi(x,y)}F(x,y)$, where the function $\phi(x,y)$ depends on both…
This paper is a continuation of our investigation of the anisotropic conformal change of a conic pseudo-Finsler surface $(M,F)$, namely, the change $\overline{F}(x,y)=e^{\phi(x,y)}F(x,y)$ \cite{first paper}. We obtain the relationship…
In this paper, for Finsler surfaces, we prove that the T-condition and $\sigma T$-condition coincide. For higher dimensions $n\geq 3$, we illustrate by an example that the T-condition and $\sigma T$-condition are not equivalent. We show…
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,…
We study a special class of Finsler metrics which we refer to as Almost Rational Finsler metrics (shortly, AR-Finsler metrics). We give necessary and sufficient conditions for an AR-Finsler manifold $(M,F)$ to be Riemannian. The rationality…
In this paper, as an application of the inverse problem of calculus of variations, we investigate two compatibility conditions on the spherically symmetric Finsler metrics. By making use of these conditions, we focus our attention on the…
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 present paper is a continuation of a foregoing paper [Tensor, N. S., 69 (2008), 155-178]. The main aim is to establish \emph{an intrinsic investigation} of the conformal change of the most important special Finsler spaces, namely,…
We show that the inclusion of a term $C_{abcd}C^{abcd}$ in the action can remove the recently described anisotropic singularity occurring on the hypersurface $F(\phi)=0$ of scalar-tensor theories of gravity of the type $$ S=\int d^4x…
We undertake to show how the relativistic Finslerian Metric Function (FMF) should arise under uni-directional violation of spatial isotropy, keeping the condition that the indicatrix (mass-shell) is a space of constant negative curvature.…
In the present paper, we find out necessary and sufficient conditions for a Finsler surface $(M,F)$ to be Landsbregian in terms of the Berwald curvature $2$-forms. We study Finsler surfaces which satisfy some flag curvature $K$ conditions,…
We investigate the necessary conditions for the two spacetimes, which are solutions to the Einstein field equations with an anisotropic matter source, to be related to each other by means of a conformal transformation. As a result, we…
In the present paper we have considered h-Randers conformal change of a Finsler metric $ L $, which is defined as \begin{center}$ L(x,y)\rightarrow \bar{L}(x, y)=e^{\sigma(x)}L(x, y)+\beta (x, y), \end{center} where $ \sigma(x) $ is a…
In this paper, we study isoparametric hypersurfaces in Finsler space forms by investigating focal points, tubes and parallel hypersurfaces of submanifolds. We prove that the focal submanifolds of isoparametric hypersurfaces are…
In this paper, we study a new class of Finsler metrics, F=\alpha\phi(b^2,s), s:=\beta/\alpha, defined by a Riemannian metric \alpha and 1-form \beta. It is called general (\alpha, \beta) metric. In this paper, we assume \phi be coefficient…
The main aim of this paper is to obtain analytic relativistic anisotropic spherical solutions in f(R,$\mathcal{T}$) scenario. To do so we use modified Durgapal-Fuloria metric potential and the isotropic condition is imposed in order to…
We study the isoperimetric problem for anisotropic left-invariant perimeter measures on $\mathbb R^3$, endowed with the Heisenberg group structure. The perimeter is associated with a left-invariant norm $\phi$ on the horizontal…
The space of anisotropic $r$-contravariant $s$-covariant $\alpha$-homogeneous tensors on a manifold admits a functorial structure where vertical derivatives $\dot{\partial}$ and contractions $\imath_{\mathbb{C}}$ by the Liouville vector…
The problem of conformal transformation and conformal flatness of Finsler spaces has been studied by so many researchers $\left[ 6,16,17,20,21\right] .$ Recently, Prasad et. al $\left[ 19\right] $ have studied three dimensional conformally…
Given a Finslerian metric $F$ on a $C^4$-manifold, conformal deformations of $F$ preserving the $R$-Einstein criterion are presented. In particular, locally conformal invariance between two Finslerian $R$-Einstein metrics is characterized.