共查询到20条相似文献,搜索用时 312 毫秒
1.
Bucataru Ioan Milkovszki Tamás Muzsnay Zoltán 《Mediterranean Journal of Mathematics》2016,13(6):4567-4580
In this paper, we study the invariant metrizability and projective metrizability problems for the special case of the geodesic spray associated to the canonical connection of a Lie group. We prove that such canonical spray is projectively Finsler metrizable if and only if it is Riemann metrizable. This result means that this structure is rigid in the sense that considering left invariant metrics, the potentially much larger class of projective Finsler metrizable canonical sprays, corresponding to Lie groups, coincides with the class of Riemann metrizable canonical sprays. Generalisation of these results for geodesic orbit spaces are given.
相似文献2.
One important problem in Finsler geometry is that of classifying Finsler metrics of scalar curvature. By investigating the second-order differential equation for a class of Randers metrics with isotropic S-curvature, we give a global classification of these metrics of scalar curvature, generalizing a theorem previously only known in the case of locally projectively flat Randers metrics. 相似文献
3.
Benling Li 《Differential Geometry and its Applications》2013,31(6):718-724
In this paper, we study the locally dually flat Finsler metrics which arise from information geometry. An equivalent condition of locally dually flat Finsler metrics is given. We find a new method to construct locally dually flat Finsler metrics by using a projectively flat Finsler metric under the condition that the projective factor is also a Finsler metric. Finally, we find that many known Finsler metrics are locally dually flat Finsler metrics determined by some projectively flat Finsler metrics. 相似文献
4.
5.
Christopher J. Catone 《Differential Geometry and its Applications》2008,26(4):404-418
In this paper we ask when a Finsler surface is projectively equivalent to a given Riemannian surface and when is a Finsler surface projectively equivalent to some Riemannian surface in general. We obtain a necessary and sufficient condition for projective equivalence in both cases. We then consider the latter condition in terms of the Christoffel symbols of the Riemannian metric and investigate when six functions of two variables are the Christoffel symbols of a Riemannian metric. We employ an exterior differential system to analyze when four functions of two variables are the four projective quantities of a Riemannian metric. We end the paper with a theorem which applies the necessary and sufficient condition to 2-dimensional Randers metrics. 相似文献
6.
In this paper, we consider a class of Finsler metrics which obtained by Kropina change of the class of generalized m-th root Finsler metrics. We classify projectively flat Finsler metrics in this class of metrics. Then under a condition, we show that every projectively flat Finsler metric in this class with constant flag curvature is locally Minkowskian. Finally, we find necessary and sufficient condition under which this class of metrics be locally dually flat. 相似文献
7.
A. Asanjarani 《Differential Geometry and its Applications》2008,26(4):434-444
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 constant sectional curvature, not necessarily of Randers type nor projectively flat, are found. This work generalizes some results in Riemannian geometry and open up, a vast area of research on Finsler geometry. 相似文献
8.
In this paper, we study spherically symmetric Finsler metrics. Analyzing the solution of the projectively flat equation, we construct a new class of projectively flat Finsler metrics. 相似文献
9.
It is known that every locally projectively flat Finsler metric is of scalar flag curvature. Conversely, it may not be true. In this paper, for a certain class of Finsler metrics, we prove that it is locally projectively flat if and only if it is of scalar flag curvature. Moreover, we establish a class of new non-trivial examples. 相似文献
10.
In this paper, we give the equivalent PDEs for projectively flat Finsler metrics with constant flag curvature defined by a Euclidean metric and two 1-forms. Furthermore, we construct some classes of new projectively flat Finsler metrics with constant flag curvature by solving these equivalent PDEs. 相似文献
11.
Xiaohuan Mo 《Israel Journal of Mathematics》2011,184(1):59-78
This paper gives an explicit construction of a family of projectively flat Finsler metrics by using hypergeometric functions
and a special class of projectively flat Randers metrics. 相似文献
12.
In this paper, we study a class of Finsler metrics in the form F = α + ∈β + 2k β2/α-k2β4/3α3 , where α= (√aijyiyj) is a Riemannian metric, β = biyi is a 1-form, and ∈ and k ≠ 0 are constants. We obtain a sufficient and necessary condition for F to be locally projectively flat and give the non-trivial special solutions. Moreover, it is proved that such projectively flat Finsler metrics with the constant flag curvature must be locally Minkowskian. 相似文献
13.
14.
Ying Li & Wei-Dong Song 《数学研究》2016,49(1):57-63
A class of Finsler metrics with three parameters is constructed. Moreover,
a sufficient and necessary condition for this Finsler metrics to be projectively flat was
obtained. 相似文献
15.
In this paper we introduce in study the projectively related complex Finsler metrics. We prove the complex versions of the Rapcsák’s theorem and characterize the weakly Kähler and generalized Berwald projectively related complex Finsler metrics. The complex version of Hilbert’s Fourth Problem is also pointed out. As an application, the projectiveness of a complex Randers metric is described. 相似文献
16.
《中国科学 数学(英文版)》2020,(7)
One of the fundamental problems in Finsler geometry is to study Finsler metrics of constant(or scalar) curvature. In this paper, we refine and improve Chen-Shen-Zhao equations characterizing Finsler warped product metrics of scalar flag curvature. In particular, we find equations that characterize Finsler warped product metrics of constant flag curvature. Then we improve the Chen-Shen-Zhao result on characterizing Einstein Finsler warped product metrics. As its application we construct explicitly many new warped product Douglas metrics of constant Ricci curvature by using known locally projectively flat spherically symmetric metrics of constant flag curvature. 相似文献
17.
In this paper, we study the problem whether a Finsler metric of scalar flag curvature is locally projectively flat. We consider a special class of Finsler metrics — square metrics which are defined by a Riemannian metric and a 1-form on a manifold. We show that in dimension n ≥ 3, any square metric of scalar flag curvature is locally projectively flat. 相似文献
18.
In this paper, we investigate the flag curvature of a special class of Finsler metrics called general spherically symmetric Finsler metrics, which are defined by a Euclidean metric and two related 1-forms. We find equations to characterize the class of metrics with constant Ricci curvature (tensor) and constant flag curvature. Moreover, we study general spherically symmetric Finsler metrics with the vanishing non-Riemannian quantity χ-curvature. In particular, we construct some new projectively flat Finsler metrics of constant flag curvature. 相似文献
19.
In this paper, we discuss the relationship between the flag curvature and some non-Riemannian quantities of Finsler metrics of scalar curvature. In particular, we characterize projectively flat Finsler metrics with isotropic S-curvature. 相似文献
20.
关于射影平坦Finsler空间 总被引:4,自引:0,他引:4
本文研究了射影平坦Finsler空间的几何量及其几何性质。证明了射影平坦Finsler空间的Ricci曲率可完全由射影因子简洁地刻画出来。同时还证明了,在射影平坦Finsler空间中,平均Berwald曲率S=0意味着Ricci曲率Ric是二次齐次的。此外,给出了一个射影平坦Finsler空间成为常曲率空间或局部Minkowski空间的充分条件。 相似文献