27 Citations
On the Finsler Geometry of Four-Dimensional Einstein Lie Groups
- 2018
Mathematics
AbstractIn this paper, we study left invariant $$(\alpha ,\beta )$$(α,β)-metrics on four-dimensional real Lie groups equipped with left invariant Einstein Riemannian metrics. We classify all left…
On Einstein Matsumoto metrics
- 2014
Physics, Mathematics
The 3-dimensional rigidity theorem is proved for a (weak) Einstein Matsumoto metric if and only if α is Ricci flat and β is a parallel 1-form with respect to α.
Invariant Einstein Kropina metrics on Lie groups and homogeneous spaces.
- 2018
Mathematics
In this article, we study Einstein Kropina metrics on Lie groups and homogeneous spaces. We give a simple way to build the Einstein Kropina metrics on Lie groups. As an example of this method, we…
On the Existence of Homogeneous Geodesics in Homogeneous Kropina Spaces
- 2019
Mathematics
Recently, it is shown that each regular homogeneous Finsler space M admits at least one homogeneous geodesic through any point $$o\in M$$ o ∈ M . The purpose of this article is to study the existence…
On the Finsler Geometry of Four-Dimensional Einstein Lie Groups
- 2019
Mathematics
In this paper, we study left invariant $$(\alpha ,\beta )$$
-metrics on four-dimensional real Lie groups equipped with left invariant Einstein Riemannian metrics. We classify all left invariant…
On Kropina metrics
- 2014
Mathematics
In this paper we study the curvature properties of Kropina metric. We find expressions for Riemann curvature and Ricci curvature of a Kropina metric when the 1-form $$\beta $$ is a Killing form of…
On Kropina metrics
- 2013
Mathematics
In this paper we study the curvature properties of Kropina metric. We find expressions for Riemann curvature and Ricci curvature of a Kropina metric when the 1-form \documentclass[12pt]{minimal}…
ON PROJECTIVE RICCI FLAT KROPINA METRICS
- 2017
Mathematics
In this paper, we study and characterize projective Ricci flat Kropina metrics. By using the formulas of S-curvature and Ricci curvature for Kropina metrics, we obtain the formula of the projective…
18 References
A class of Einstein (α, β)-metrics
- 2012
Mathematics, Physics
In this paper, we study a special class of Finsler metrics, called (α, β)-metrics, which are defined by F = αϕ(β/α), where α is a Riemannian metric and β is a 1-form. We show that if ϕ = ϕ(s) is a…
Finsler Geometry, Relativity and Gauge Theories
- 1985
Physics, Mathematics
A. Motivation and Outline of the Book.- B. Introduction to Finsler Geometry.- 1/Primary Mathematical Definitions.- 1.1. Concomitants of the Finslerian Metric Function.- 1.2. The Indicatrix.- 1.3. The…
Ricci and Flag Curvatures in Finsler Geometry
- 2004
Mathematics
Introduction 198 1. Flag and Ricci Curvatures 199 1.1. Finsler metrics 199 1.2. Flag curvature 207 1.3. Ricci curvature 214 2. Randers Metrics in Their Defining Form 218 2.1. Basics 218 2.2.…
ON A CLASS OF PROJECTIVELY FLAT FINSLER METRICS WITH CONSTANT FLAG CURVATURE
- 2007
Mathematics
In this paper, we study a class of Finsler metrics defined by a Riemannian metric and a 1-form. We classify those projectively flat with constant flag curvature.
On projective two-dimensional Finsler spaces with special metric
- 2006
Mathematics
We present the English translation of the paper where one special class of Finsler spaces was introduced. Now this class is known as so called "Kropina spaces". The article was written in 1958 and…
Zermelo navigation on Riemannian manifolds
- 2003
Mathematics
In this paper, we study Zermelo navigation on Riemannian manifolds and use that to solve a long standing problem in Finsler geometry, namely the complete classification of strongly convex Randers…
Riemann-Finsler geometry
- 2005
Mathematics, Physics
# Finsler Metrics # Structure Equations # Geodesics # Parallel Translations # S-Curvature # Riemann Curvature # Finsler Metrics of Scalar Flag Curvature # Projectively Flat Finsler Metrics
On Finsler geometry
- 1992
Mathematics
On introduit une connexion nouvelle dans un espace de Finsler, qui resout en meme temps le probleme de l'equivalence. Dans cette connexion la courbure se partage en deux parties, dites respectivement…