相关论文: Two-dimensional Finsler metrics of constant curvat…

In Finsler geometry, there are infinitely many models of constant curvature. The Funk metrics, the Hilbert-Klein metrics and the Bryant metrics are projectively flat with non-zero constant curvature. A recent example constructed by the…

It is the Hilbert's Fourth Problem to characterize the (not-necessarily-reversible) distance functions on a bounded convex domain in R^n such that straight lines are shortest paths. Distance functions induced by a Finsler metric are…

In this paper, we study locally projectively flat Finsler metrics with constant flag curvature ${\bf K}$. We prove those are totally determined by their behaviors at the origin by solving some nonlinear PDEs. The classifications when ${\bf…

I classify the Finsler structures on the 2-sphere that have constant Finsler-Gauss curvature and whose geodesics are the great circles. Modulo diffeomorphism, there is a 2-parameter family of such Finsler structures, only one of which is…

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…

In this paper we study a class of Finsler metrics defined by a Riemannian metric and an 1-form. We classify those of projectively flat in dimension $n\geq3$ by a special class of deformations. The results show that the projective flatness…

This article is an exposition of four loosely related remarks on the geometry of Finsler manifolds with constant positive flag curvature. <p> The first remark is that there is a canonical Kahler structure on the space of geodesics of such a…

We investigate projective spherically symmetric Finsler metrics with constant flag curvature in $R^n$ and give the complete classification theorems. Furthermore, a new class of Finsler metrics with two parameters on n-dimensional disk are…

In this paper we study the flag curvature of a particular class of Finsler metrics called general $(\alpha,\beta)$-metrics, which are defined by a Riemannian metric $\alpha$ and a $1$-form $\beta$. The classification of such metrics with…

Hilbert's fourth problem seeks the classification of metric geometries where straight lines are shortest paths. Its regular case identifies the projectively flat Finsler manifolds. This broader framework breaks the equivalence between…

We construct a concrete example of constant Gauss curvature $K = 1$ on the 2-sphere having all geodesics closed and of same length.

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, studying the inverse problem, we establish a curvature compatibility condition on a spherically symmetric Finsler metric. As an application, we characterize the spherically symmetric metrics of scalar curvature. We construct…

By using a certain second order differential equation, the notion of adapted coordinates on Finsler manifolds is defined and some classifications of complete Finsler manifolds are found. Some examples of Finsler metrics, with positive…

Singular Finsler metrics, such as Kropina metrics and $m$-Kropina metrics, have a lot of applications in the real world. In this paper, we classify a class of singular $(\alpha,\beta)$-metrics which are locally projectively flat with…

In this paper, we give the general form of spherically symmetric Finsler metrics in $R^n$ and surprisedly find that many well-known Finsler metrics belong to this class. Then we explicitly express projective metrics of this type. The…

The well-known Funk metric F(x,y) is projectively flat with constant flag curvature K=-1/4 and the Hilbert metric H(x,y):=(F(x,y)+F(x,-y))/2 is projectively flat with constant curvature K=-1. These metrics are the special solutions to…

If the flag curvature of a Finsler manifold reduces to sectional curvature, then locally either the Finsler metric is Riemannian, or the flag curvature is isotropic.

The class of spherically symmetric Finsler metrics is studied and locally dually flat and projectively flat spherically symmetric Finsler metrics is classified.

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…