共查询到20条相似文献,搜索用时 31 毫秒
1.
The S-curvature is one of most important non-Riemannian quantities in Finsler geometry. It delicately related to Riemannian quantities. This note gives an explicit construction of 3-parameter family of non-locally projectively flat Finsler metrics of non-constant isotropic S-curvature. The necessary and sufficient condition that these Finsler metrics are of constant flag curvature is given. 相似文献
2.
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
3.
In this paper, we study a class of Finsler metrics defined by a vector field on a Riemannian space form. We give an explicit formula for those with isotropic S-curvature. This class contains all Randers metrics of constant flag curvature. 相似文献
4.
In this paper, we study Finsler metrics of scalar flag curvature. We find that a non-Riemannian quantity is closely related
to the flag curvature. We show that the flag curvature is weakly isotropic if and only if this non-Riemannian quantity takes
a special form. This will lead to a better understanding on Finsler metrics of scalar flag curvature.
相似文献
5.
Linfeng Zhou 《Geometriae Dedicata》2012,158(1):353-364
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 is found to have constant negative flag curvature. 相似文献
6.
In this paper, we will give a complete classification of homogeneous Randers spaces with isotropic S-curvature and positive flag curvature. This results in a large class of Finsler spaces with non-constant positive flag curvature. At the final part of the paper, we prove a rigidity result asserting that a homogeneous Randers space with almost isotropic S-curvature and negative Ricci scalar must be Riemannian. 相似文献
7.
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
8.
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 with Ric = 2F 2, Ric = 0 and Ric = -2F 2, respectively. This family of metrics provides an important class of Finsler metrics in dimension three, whose Ricci curvature is a constant, but the flag curvature is not. 相似文献
9.
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
10.
The local structure of Finsler metrics of constant flag curvature have been historically mysterious. It is proved that every Matsumoto metric of constant flag curvature on a closed n-dimensional manifold of dimension n ≥ 3 is either Riemannian or locally Minkowskian. 相似文献
11.
Projectively flat Finsler metrics of constant flag curvature 总被引:8,自引:0,他引:8
Zhongmin Shen 《Transactions of the American Mathematical Society》2003,355(4):1713-1728
Finsler metrics on an open subset in with straight geodesics are said to be projective. It is known that the flag curvature of any projective Finsler metric is a scalar function of tangent vectors (the flag curvature must be a constant if it is Riemannian). In this paper, we discuss the classification problem on projective Finsler metrics of constant flag curvature. We express them by a Taylor expansion or an algebraic formula. Many examples constructed in this paper can be used as models in Finsler geometry.
12.
13.
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
14.
Xiaohuan Mo 《中国科学A辑(英文版)》1998,41(9):910-917
The geometric characterization and structure of Finsler manifolds with constant flag curvature (CFC) are studied. It is proved
that a Finsler space has constant flag curvature 1 (resp. 0) if and only if the Ricci curvature along the Hilbert form on
the projective sphere bundle attains identically its maximum (resp. Ricci scalar). The horizontal distributionH of this bundle is integrable if and only ifM has zero flag curvature. When a Finsler space has CFC, Hilbert form’s orthogonal complement in the horizontal distribution
is also integrable. Moreover, the minimality of its foliations is equivalent to given Finsler space being Riemannian, and
its first normal space is vertical
Project supported by Wang KC Fundation of Hong Kong and the National Natural Science Foundation of China (Grant No. 19571005). 相似文献
15.
Xiaohuan Mo 《Differential Geometry and its Applications》2009,27(1):7-14
One of fundamental problems in Finsler geometry is to establish some delicate equations between Riemannian invariants and non-Riemannian invariants. Inspired by results due to Akbar-Zadeh etc., this note establishes a new fundamental equation between non-Riemannian quantity H and Riemannian quantities on a Finsler manifold. As its application, we show that all R-quadratic Finsler metrics have vanishing non-Riemannian invariant H generalizing result previously only known in the case of Randers metric. 相似文献
16.
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
17.
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
18.
《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
19.
Without the restriction of quadratic form as a Riemannian metric, a Finsler metric on a smooth manifold M can be reversible (symmetric in y) or not. Reversible Finsler metrics have different properties from Riemannian metrics though it seems they are very close to Riemannian metrics. Hilbert metric is the famous reversible Finsler metric of negative constant flag curvature in the history, and it is projectively flat. Then it is natural to ask the question how to classify reversible projectively flat Finsler metrics of constant flag curvature and give more new examples? In this paper, we answer the above question by giving the classification when the flag curvature respectively. Especially, for the case when , we show that the only reversible projectively flat Finsler metrics are just Hilbert metrics. For the case when , we give an algebraic way to construct explicit metric function by solving algebraic equations, such as by solving a quartic equation. When the flag curvature is zero, it is much easier to construct reversible projectively flat Finsler metrics than before. 相似文献