共查询到20条相似文献,搜索用时 953 毫秒
1.
本文研究共形平坦的Randers 度量的性质. 证明了具有数量旗曲率的共形平坦的Randers 度量都是局部射影平坦的, 并且给出了这类度量的分类结果. 本文还证明了不存在非平凡的共形平坦且具有近迷向S 曲率的Randers 度量. 相似文献
2.
3.
本文研究和刻画了射影Ricci平坦的Kropina度量.利用Kropina度量的S-曲率和Ricci曲率的公式,得到了Kropina度量的射影Ricci曲率公式.在此基础上得到了Kropina度量是射影Ricci平坦度量的充分必要条件.进一步,作为自然的应用,本文研究和刻画了由一个黎曼度量和一个具有常数长度的Killing 1-形式定义的射影Ricci平坦的Kropina度量,也刻画了具有迷向S-曲率的射影Ricci平坦的Kropina度量.在这种情形下,Kropina度量是Ricci平坦度量. 相似文献
4.
局部射影平坦芬斯勒度量的构造是芬斯勒几何研究中的一个重要问题.本文通过对球对称芬斯勒度量成为射影平坦芬斯勒度量所满足的偏微分方程进行研究,得到了局部射影平坦芬斯勒度量的新例子.进一步,给出了局部射影平坦的球对称芬斯勒度量的旗曲率. 相似文献
5.
6.
针对拟对称(α,β)-度量,致力于研究拟对称(α,β)-度量局部射影平坦的等价条件,以及局部射影平坦的拟对称(α,β)-度量所具有的旗曲率性质. 相似文献
7.
利用Hamel关于射影平坦的基本方程,我们导出了Randers度量的λ形变保持射影平坦的充分条件.特别,对一类具有特殊旗曲率性质的Randers度量我们证明了这类度量一定存在保持射影平坦性的λ形变. 相似文献
8.
研究刻画球对称Finsler度量的射影平坦性质的偏微分方程,通过对射影平坦Finsler度量PDE的研究,构造了两类球对称射影平坦Finsler度量,得到了一些球对称的射影平坦Finsler度量,并进一步给出这些Finsler度量的射影因子和旗曲率. 相似文献
9.
10.
11.
In this paper, we study and characterize locally projectively flat singular square metrics with constant flag curvature. First, we obtain the sufficient and necessary conditions that singular square metrics are locally projectively flat. Furthermore, we classify locally projectively flat singular square metrics with constant flag curvature completely. 相似文献
12.
Guo Jun Yang 《数学学报(英文版)》2013,29(5):959-974
In this paper, we study a special class of two-dimensional Finsler metrics defined by a Riemannian metric and 1-form. We classify those which are locally projectively flat with constant flag curvature. 相似文献
13.
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
14.
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
15.
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
16.
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
17.
Projectively flat Randers metrics with constant flag curvature 总被引:2,自引:0,他引:2
Zhongmin Shen 《Mathematische Annalen》2003,325(1):19-30
We classify locally projectively flat Randers metrics with constant Ricci curvature and obtain a new family of Randers metrics
of negative constant flag curvature.
Received: 19 July 2001 / Revised version: 15 March 2002 / Published online: 16 October 2002 相似文献
18.
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 give the classification of the holonomy groups of locally projectively flat Randers two-manifolds of constant curvature. In particular, we prove that the holonomy group of a simply connected non-Riemannian projectively flat Finsler two-manifold of constant non-zero flag curvature is maximal and isomorphic to the orientation preserving diffeomorphism group of the circle. 相似文献
19.
In this paper we study a special class of Finsler metrics—m-Kropina metrics which are defined by a Riemannian metric and a 1-form. We prove that a weakly Einstein m-Kropina metric must be Einsteinian. Further, we characterize Einstein m-Kropina metrics in very simple conditions under a suitable deformation, and obtain the local structures of m-Kropina metrics which are of constant flag curvature and locally projectively flat with constant flag curvature respectively. 相似文献
20.
《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