Related papers: On Landsberg general $(\alpha,\beta)$-metrics with…
In the paper we consider two Finsler-like Riemannian metrics, which can be in a natural way introduced into general relativity. One of those metrics $\gamma_{ab}$ is degenerate and the second $h_{ab}$ is nondegenerate. We are mainly…
Here, it is introduced a concept of convolution metric in Finslerian Geometry. This convolution metric is a kind of function obtained by a given mathematical operation between two Finslerian metrics. Some basic properties of the Finslerian…
A Finsler metric is geodesically reversible if geodesics remain geodesics after a change of orientation. Asymmetric norms on vector spaces and Funk metrics in the interior of convex bodies are examples of geodesically reversible metrics…
We investigate the relation between weighted quasi-metric Spaces and Finsler Spaces. We show that the induced metric of a Randers space with reversible geodesics is a weighted quasi-metric space.
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…
A locally conformal SKT (shortly LCSKT) structure is a Hermitian structure $(J, g)$ whose Bismut torsion 3-form $H$ satisfies the condition $dH = \alpha \wedge H$, for some closed non-zero 1-form $\alpha$. This condition was introduced in…
We study the irregularity sheaves attached to the $A$-hypergeometric $D$-module $M_A(\beta)$ introduced by Gel'fand et al., where $A\in\mathbb{Z}^{d\times n}$ is pointed of full rank and $\beta\in\mathbb{C}^d$. More precisely, we…
We introduce and study a novel uniformization metric model for the quasi-Fuchsian space QF(S) of a closed oriented surface S, defined through a class of C-valued bilinear forms on S, called Bers metrics, which coincide with hyperbolic…
In this Note, we prove that every m-th root Finsler metric with isotropic Landsberg curvature reduces to a Landsberg metric. Then, we show that every m-th root metric with almost vanishing H-curvature has vanishing H-curvature.
In this paper, we study geodesics and geodesic vectors for homogeneous exponential Finsler space and homogeneous infinite series Finsler space. Further, we find necessary and sufficient condition for a non-zero vector in these homogeneous…
In this paper, the necessary and sufficient conditions for Matsumoto metrics $F=\frac{\alpha^2}{\alpha-\beta}$ to be Einstein are given. It is shown that if the length of $\beta$ with respect to $\alpha$ is constant, then the Matsumoto…
The main object of this paper is to present a new generalized beta function which defined by three parametres Mittag-Leffler function. We also introduce new generalizations of hypergeometric and confluent hypergeometric functions with the…
Singular Finsler metrics, such as Kropina metrics and $m$-Kropina metrics, have a lot of applications in the real world. In this paper, we study a class of singular Finsler metrics defined by a Riemann metric $\alpha$ and 1-form $\beta$ and…
Berwald metrics are particular Finsler metrics which still have linear Berwald connections. Their complete classification is established in an earlier work, [Sz1], of this author. The main tools in these classification are the Simons-Berger…
The study of curvature properties of homogeneous Finsler spaces with $(\alpha, \beta)$-metrics is one of the central problems in Riemann-Finsler geometry. In this paper, we consider homogeneous Finsler spaces with square metric and Randers…
Square metrics $F=\frac{(\alpha+\beta)^2}{\alpha}$ are a special class of Finsler metrics. It is the rate kind of metric category to be of excellent geometrical properties. In this paper, we discuss the so-called singular square metrics…
In this article, we review some aspects of gravitational field and cosmology based on Finsler and Finsler-like generalized metric structures. The geometrical framework of these spaces allows further investigation of locally-anisotropic…
A gap in the proof of the finsler "unicorn" conjecture in the paper "Regular Landsberg metrics are always Berwald" by Z. I. Szabo is pointed out
This article deals with the ratio of normalized Mittag-Leffler function $\mathbb{E}_{\alpha,\beta}(z)$ and its sequence of partial sums $(\mathbb{E}_{\alpha,\beta})_m(z)$. Several examples which illustrate the validity of our results are…
In this paper, we presented a new type of metric space called $(\alpha,\beta)$-metric space along with some novel contraction mappings named $(\alpha,\beta)$-contraction and weak $(\alpha,\beta)$-contraction mapping. We established some…