Related papers: Cyclic Finser metrics on homogeneous spaces

In this paper, we establish a sufficient condition for a geodesic in a Riemannian manifold to be homogeneous, i.e. an orbit of an $1$-parameter isometry group. As an application of this result, we provide a new proof of the fact that every…

A method to generalize results from Riemannian Geometry to Finsler geometry is presented. We use the method to generalize several results that involve only metric conditions. Between them we show that the topology induced by the Finsler…

We study extrinsic geometry of a codimension-one foliation ${\cal F}$ of a closed Finsler space $(M,F)$, in particular, of a Randers space $(M,\alpha+\beta)$. Using a unit vector field $\nu$ orthogonal (in the Finsler sense) to the leaves…

A new geometrical definition of naturally reductive Finsler manifold using geodeic graph is proposed, with a possible generalization. Based on a construction from a recent paper by the authors, Finsler metrics based on naturally reductive…

Let $F$ be a homogeneous $(\alpha_1,\alpha_2)$ metric on the reductive homogeneous manifold $G/H$. Firstly, we characterize the natural reductiveness of $F$ as a local $f$-product between naturally reductive Riemannian metrics. Secondly, we…

We consider a homogeneous fibration $G/L \to G/K$, with symmetric fiber and base, where $G$ is a compact connected semisimple Lie group and $L$ has maximal rank in $G$. We suppose the base space $G/K$ is isotropy irreducible and the fiber…

In this paper, we consider Randers change of some special $ (\alpha, \beta)- $ metrics. First we find the fundamental metric tensor and Cartan tensor of these Randers changed $ (\alpha, \beta)- $metrics. Next, we establish a general formula…

In this paper, first, we give an explicit formula for the flag curvature of a homogeneous Finsler space with generalized $m$-Kropina metric. Then, we show that, under a mild condition, the two definitions of naturally reductive homogeneous…

A Clifford-Wolf translation of a connected Finsler space is an isometry which moves each point the sam distance. A Finsler space $(M, F)$ is called Clifford-Wolf homogeneous if for any two point $x_1, x_2\in M$ there is a Clifford-Wolf…

First we present a short overview of the long history of projectively flat Finsler spaces. We give a simple and quite elementary proof of the already known condition for the projective flatness, and we give a criterion for the projective…

We give a complete classification of homogeneous $(\alpha,\beta)$-metrics with positive flag curvature and vanishing S-curvature.

In this paper, we prove that a strongly convex complex Finsler metric $F$ on a domain $D\subset\mathbb{C}^n$ is projectively flat (resp. dually flat) if and only if $F$ comes from a strongly convex complex Minkowski metric.

We prove that a generically regular semisimple Higgs bundle equipped with a non-degenerate symmetric pairing on any Riemann surface always has a harmonic metric compatible with the pairing. We also study the classification of such…

The notion of $\Gamma$-symmetric space is a natural generalization of the classical notion of symmetric space based on $\Z_2$-grading of Lie algebras. In our case, we consider homogeneous spaces $G/H$ such that the Lie algebra $\g$ of $G$…

In this paper we study isometry-invariant Finsler metrics on inner product spaces over $\mathbb{R}$ or $\mathbb{C}$, i.e. the Finsler metrics which do not change under the action of all isometries of the inner product space. We give a new…

In this paper, we introduce an asymmetric metric on the space of marked Euclidean triangles, and we prove several properties of this metric, including two equivalent definitions of this metric, one of them comparing ratios of functions of…

When a closed Finsler manifold admits continuous isometric actions, estimating the number of orbits of prime closed geodesics seems a more reasonable substitution for estimating the number of prime closed geodesics. To generalize the works…

A piecewise flat Finsler metric on a triangulated surface $M$ is a metric whose restriction to any triangle is a flat triangle in some Minkowski space with straight edges. One of the main purposes of this work is to study the properties of…

The notion of $\Gamma$-symmetric space is a natural generalization of the classical notion of symmetric space based on $\z_2$-grading of Lie algebras. In our case, we consider homogeneous spaces $G/H$ such that the Lie algebra $\g$ of $G$…

In this paper, we classify the spherically symmetric Berwald metrics in $\mathbb{R}^n$. For the spherically symmetric Landsberg metrics, we prove that there do not exist any non-Berwald metrics among the regular case. The partial…