Related papers: Clifford-Wolf homogeneous Randers spaces

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…

An isometry of a Finsler space is called Clifford-Wolf translation (CW-translation) if it moves all points the same distance. A Finsler space $(M, F)$ is called Clifford-Wolf homogeneous (CW-homogeneous) if for any $x, y\in M$ there is a…

This paper has been withdrawn by the author due to a crucial sign error in equation 1. An isometry $\rho$ of a connected Finsler space $(M, F)$ is called bounded if the function $d(x, \rho(x))$ is bounded on $M$. It is called a…

Let $(M,F)$ be a connected Finsler space and $d$ the distance function of $(M,F)$. A Clifford translation is an isometry $\rho$ of $(M,F)$ of constant displacement, in other words such that $d(x,\rho(x))$ is a constant function on $M$. In…

In this paper, we study Clifford-Wolf translations of Finsler spaces. We first give a characterization of Clifford-Wolf translations of Finsler spaces in terms of Killing vector fields. In particular, we show that there is a natural…

Let $(M,F)$ be a connected Finsler space. An isometry of $(M,F)$ is called a Clifford-Wolf translation (or simply CW-translation) if it moves all points the same distance. The compact Finsler space $(M,F)$ is called restrictively…

In this paper, we study Clifford-Wolf translations of homogeneous Randers metrics on spheres. It turns out that we can present a complete description of all the Clifford-Wolf translations of all the homogeneous Randers metrics on spheres.…

In this paper, we introduce a new type of Finsler metrics, called $(\alpha_1,\alpha_2)$-metrics. We define the notion of the good datum of a homogeneous $(\alpha_1,\alpha_2)$-metric and use that to study the geometric properties. In…

In this paper, using connections between Clifford-Wolf isometries and Killing vector fields of constant length on a given Riemannian manifold, we classify simply connected Clifford-Wolf homogeneous Riemannian manifolds. We also get the…

A Finsler space is called Ricci-quadratic if its Ricci curvature $Ric(x,y)$ is quadratic in $y$. It is called a Berwald space if its Chern connection defines a linear connection directly on the underlying manifold $M$. In this article, we…

We show that if a Finsler space is conformally automorphic to a Riemannian space and the automorphism is positively homogeneous with respect to tangent vectors, then the indicatrix of the Finsler space is a space of constant curvature. In…

The Finsler spaces in which the tangent Riemannian spaces are conformally flat prove to be characterized by the condition that the indicatrix is a space of constant curvature. In such spaces the Finslerian normalized two-vector angle can be…

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.…

A linear connection on a Finsler manifold is called compatible to the metric if its parallel transports preserve the Finslerian length of tangent vectors. Generalized Berwald manifolds are Finsler manifolds equipped with a compatible linear…

In this paper, we explore the similarity between normal homogeneity and $\delta$-homogeneity in Finsler geometry. They are both non-negatively curved Finsler spaces. We show that any connected $\delta$-homogeneous Finsler space is…

A smooth curve on a homogeneous manifold $G/H$ is called a Riemannian equigeo-desic if it is a homogeneous geodesic for any $G$-invariant Riemannian metric. The homogeneous manifold $G/H$ is called Riemannian equigeodesic, if for any $x\in…

In this paper, we investigate the holonomy structure of the most accessible and demonstrative 2-dimensional Finsler surfaces, the Randers surfaces. Randers metrics can be considered as the solutions of the Zermelo navigation problem. We…

We survey the geometry of Lagrange and Finsler spaces and discuss the issues related to the definition of curvature of nonholonomic manifolds enabled with nonlinear connection structure. It is proved that any commutative Riemannian geometry…

We show that monochromatic Finsler metrics, i.e., Finsler metrics such that each two tangent spaces are isomorphic as normed spaces, are generalized Berwald metrics, i.e., there exists an affine connection, possibly with torsion, that…

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…