arXiv research

The paper studies Finsler spaces with semi-concurrent vector fields and their equivalence to Riemannian spaces.

The present paper deals with the Killing correspondence between some Finsler spaces. We consider a Finsler space equipped with a $β$-change of metric and study the Killing correspondence between the original Finsler space and the Finsler space equipped with $β$-change of metric. We obtain necessary and sufficient condi…

PhD dissertation on Finsler geometry and gravity, focusing on Berwald spaces and exact solutions.

The study introduces new tensors for almost Finsler manifolds and analyzes their properties.

The aim of the present paper is to provide an intrinsic investigation of two special Finsler spaces whose defining properties are related to Berwald connection, namely, Finsler space of scalar curvature and of constant curvature. Some characterizations of a Finsler space of scalar curvature are proved. Necessary and su…

The pullback approach to global Finsler geometry is adopted. Some new types of special Finsler spaces are introduced and investigated, namely, Ricci, generalized Ricci, projectively recurrent and m-projectively recurrent Finsler spaces. The properties of these special Finsler spaces are studied and the relations betwee…

In this paper, we study normal homogeneous Finsler spaces. We first define the notion of a normal homogeneous Finsler space, using the method of isometric submersion of Finsler metrics. Then we study the geometric properties. In particular, we establish a technique to reduce the classification of normal homogeneous Fin…

Study Ricci curvature of homogeneous Finsler spaces with specific metrics.

Study geometrical properties of Finsler space hypersurface with h-Matsumoto change.

The distance function $\varrho(p,q)$ (or $d(p,q)$) of a distance space (general metric space) is not differentiable in general. We investigate such distance spaces over $\mathbb R^n$, whose distance functions are differentiable like in case of Finsler spaces. These spaces have several good properties, yet they are no F…

Smooth Busemann functions found in harmonic Finsler spaces.

The paper consider the symmetric of Finsler spaces. We give some conditions about globally symmetric Finsler spaces. Then we prove that these spaces can be written as a coset space of Lie group with an invariant Finsler metric. Finally, we prove that such a space must be Berwaldian

Busemann G-spaces with Finsler metrics

Study flag curvature in homogeneous Finsler spaces with a specific metric.

A projective parameter of a geodesic on a Finsler space is defined to be solution of a certain ODE. Using projective parameter and Funk metric, one can construct a projectively invariant intrinsic pseudo-distance on a Finsler space. In the present work, solutions of the projective parameter's ODE are characterized with…

The aim of the present paper is to provide an \emph{intrinsic} investigation of special Finsler spaces of $H_{p}$-scalar curvature and of $H_{p}\,$-constant curvature. Characterizations of such spaces are shown. Sufficient condition for Finsler space of $H_{p}$-scalar curvature to be of perpendicular scalar curvature i…

The study examines Einstein-Finsler spaces using Minkowskian products.

Recently, we have studied evolution of a family of Finsler metrics along Finsler Ricci flow and proved its convergence in short time. Here, existence of solutions to the so called Hamilton Ricci flow on Finsler spaces is studied and a short time solution is found. To this end the Finslerian Ricci-DeTurck flow on Finsle…

Two special Finsler spaces have been introduced and investigated, namely $R^h$-recurrent Finsler space and consircularly recurrent Finsler space. The defining properties of these spaces are formulated in terms of the first curvature tensor of Cartan connection. The following three results constitute the main object of …

The paper extends two-step homogeneous geodesics to homogeneous Finsler spaces.

Study projective symmetries in Finsler spaces, showing reductions and constant flag curvature.

In this paper, we explore the similarity between normal homogeneity and $δ$-homogeneity in Finsler geometry. They are both non-negatively curved Finsler spaces. We show that any connected $δ$-homogeneous Finsler space is $G$-$δ$-homo-geneous, for some suitably chosen connected quasi-compact $G$. So $δ$-homogeneous Fins…

In this work an intrinsic projectively invariant distance is used to establish a new approach to the study of projective geometry in Finsler space. It is shown that the projectively invariant distance previously defined is a constant multiple of the Finsler distance in certain case. As a consequence, two projectively r…

The paper proves isoparametric functions on Finsler space forms under specific conditions.

The paper studies curves in Finsler-like spaces and their properties.

In this paper, we use the flag curvature formula for homogeneous Finsler spaces in our previous work to classify odd dimensional smooth coset spaces admitting positively curved reversible homogeneous Finsler metrics. We will show that the most features of L. Bérard-Bergery's classification results for odd dimensional p…

Locally classifies 4D spherical symmetric Finsler spaces.

The paper finds and analyzes the Funk-Finsler structure in constant curvature spaces.

The aim of the present paper is to construct and investigate a Finsler structure within the framework of a Generalized Absolute Parallelism space (GAP-space). The Finsler structure is obtained from the vector fields forming the parallelization of the GAP-space. The resulting space, which we refer to as a Finslerized Pa…

Complete Finsler spaces with negative Ricci curvature are reversible.

We prove some rigidity results on geodesic orbit Finsler spaces with non-positive curvature. In particular, we show that a geodesic Finsler space with strictly negative flag curvature must be a non-compact Riemannian symmetric space of rank one.

In this paper, first we prove the existence of invariant vector field on a homogeneous Finsler space with infinite series $(α, β)$-metric and exponential metric. Next, we deduce an explicit formula for the the $S$-curvature of homogeneous Finsler space with these metrics. Using this formula, we further derive the formu…

Here, a non-linear analysis method is applied rather than classical one to study projective Finsler geometry. More intuitively, by means of an inequality on Ricci-Finsler curvature, a projectively invariant pseudo-distance is introduced and an analogous of Schwarz' lemma in Finsler geometry is proved. Next, the Schwarz…

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. In the special case that the homogeneous Finsler space is a Randers space, we giv…

We study the divergence theorem on pseudo-Finsler spaces and obtain a completely Finslerian version for spaces having a vanishing mean Cartan torsion. This result helps to clarify the problem of energy-momentum conservation in Finsler gravity theories.

New methods for constructing submersions between different types of spaces.

The paper classifies isoparametric hypersurfaces in conic Finsler spaces.

The paper explores harmonic and asymptotically harmonic Finsler manifolds and their properties.

We explore a connection between the Finslerian area functional based on the Busemann-Hausdorff-volume form, and well-investigated Cartan functionals to solve Plateau's problem in Finsler 3-space, and prove higher regularity of solutions. Free and semi-free geometric boundary value problems, as well as the Douglas probl…

In this paper, it is shown that a large set of connections on a suitable sub-bundle of the tangent bundle of a Finsler Manifold can be used to study all the properties of convex neighbourhoods with respect to the Finsler Metric, which are needed to see that any Complete Finsler Space is Geodesically Connected.

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 spaces to be a geodesic vector.

We formulate the notion of the Finsleroid--Finsler space, including the positive--definite as well as indefinite cases. The associated concepts of angle, scalar product, and the distance function are elucidated. If the Finsleroid--Finsler space is of Landsberg type, then the Finsleroid charge is a constant. The Finsler…

Let $(M,F)$ be a connected Finsler space and $d$ the distance function of $(M,F)$. A Clifford translation is an isometry $ρ$ of $(M,F)$ of constant displacement, in other words such that $d(x,ρ(x))$ is a constant function on $M$. In this paper we consider a connected simply connected symmetric Finsler space and a discr…

Here, the concept of electric capacity on Finsler spaces is introduced and the fundamental conformal invariant property is proved, i.e. the capacity of a compact set on a connected non-compact Finsler manifold is conformal invariant. This work enables mathematicians and theoretical physicists to become more familiar wi…

The paper establishes new inequalities for Finsler measure spaces.

A particular Finsler-metric proposed in [1,2] and describing a geometry with a preferred null direction is characterized here as belonging to a subclass contained in a larger class of Finsler-metrics with one or more preferred directions (null, space- or timelike). The metrics are classified according to their group of…

Investigates hypersurfaces in Finsler spaces with generalized square metrics.

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, $C^{h}$-recurrent, $C^{v}$-recurrent, $C^{0}$-recurrent, $C_{2}$-like, quasi-$C$-redu…