相关论文: Finsler Metrics with K=0 and S=0

The goal of this paper is to introduce and study analogues of the Euclidean Funk and Hilbert metrics on open convex subsets $\Omega$ of hyperbolic or spherical spaces. At least at a formal level, there are striking similarities among the…

The flag curvature is a natural extension of the sectional curvature in Riemannian geometry, and the S-curvature is a non-Riemannian quantity which vanishes for Riemannian metrics. There are (incomplete) non-Riemannian Finsler metrics on an…

In this paper, we answer some natural questions on symmetrisation and more general combinations of Finsler metrics, with a view towards applications to Funk and Hilbert geometries and to metrics on Teichm{\"u}ller spaces. For a general…

We study non-reversible Finsler metrics with constant flag curvature 1 on S^2 and show that the geodesic flow of every such metric is conjugate to that of one of Katok's examples, which form a 1-parameter family. In particular, the length…

In this paper, we consider the cylindrically symmetric Finsler metrics and we obtain their Douglas curvature. Furthermore, we obtain the differential equation system of the cylindrically symmetric Finsler metrics with vanishing Douglas…

We show that in dimension 2 every Finsler metric with at least 3-dimensional Lie algebra of projective vector fields is locally projectively equivalent to a Randers metric. We give a short list of such Finsler metrics which is complete up…

We define a Weyl-type curvature tensor of $(1,2)$-type to provide a characterization for Finsler metrics of constant flag curvature. This Weyl-type curvature tensor is projective invariant only to projective factors that are Hamel…

We proof that on a surface of negative Euler characteristic, two real-analytic Finsler metrics have the same unparametrized oriented geodesics, if and only if they differ by a scaling constant and addition of a closed 1-form.

The flag curvature of a Finsler metric is called a Riemannian quantity because it is an extension of sectional curvature in Riemannian geometry. In Finsler geometry, there are several non-Riemannian quantities such as the (mean) Cartan…

A Finsler space is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In…

Spherically symmetric metrics form a rich and important class of metrics. Many well-known Finsler metrics of constant flag curvature can be locally expressed as a spherically symmetric metric on R^n. In this paper, we study spherically…

In this work, the dual flatness, which is connected with Statistics and Information geometry, of general $(\alpha,\beta)$-metrics (a new class of Finsler metrics) is studied. A nice characterization for such metrics to be dually flat under…

We define a Weyl-type curvature tensor that provides a characterisation for Finsler metrics of constant flag curvature. When the Finsler metric reduces to a Riemannian metric, the Weyl-type curvature tensor reduces to the classic projective…

For non-reversible Finsler metrics of positive flag curvature on spheres and projective spaces we present results about the number and the length of closed geodesics and about their stability properties.

By using the Hawking Taub-NUT metric, this note gives an explicit construction of a 3-parameter family of Einstein Finsler metrics of non-constant flag curvature in terms of navigation representation.

In this paper, we use a Killing form on a Riemannian manifold to construct a class of Finsler metrics. We find equations that characterize Einstein metrics among this class. In particular, we construct a family of Einstein metrics on $S^3$…

An $(\alpha,\beta)$-manifold $(M,F)$ is a Finsler manifold with the Finsler metric $F$ being defined by a Riemannian metric $\alpha$ and $1$-form $\beta$ on the manifold $M$. In this paper, we classify $n$-dimensional…

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…

We define a partition of the space of projectively flat metrics in three classes according to the sign of the Chern scalar curvature; we prove that the class of negative projectively flat metrics is empty, and that the class of positive…

In complex Finsler geometry, an open problem is: does there exist a weakly K\"ahler Finsler metric which is not K\"ahler? In this paper, we give an affirmative answer to this open problem. More precisely, we construct a family of the weakly…