共查询到20条相似文献,搜索用时 387 毫秒
1.
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
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《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
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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
5.
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
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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
7.
Xiaohuan Mo 《Results in Mathematics》2011,60(1-4):475-485
(α, β)-norms on ${\mathbb{R}^N}$ induce Minkowski metrics, and the construction of related homothetic vector fields gives a family of new Finsler metrics of non-positive constant flag curvature for each non-trivial (α, β)-norm. The dimension of this family is at least ${\tfrac{1}{2}(N^2 - N + 4)}$ . In particular, we generalize the Funk metric on the unit ball via navigation representation of the standard Euclidean norm and the radial vector field. Finally, we describe the geodesics of these new Finsler metrics with constant flag curvature. 相似文献
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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
9.
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 open subset in Rn with negative flag curvature and constant S-curvature. In this paper, we are going to show a global rigidity theorem that every Finsler metric with negative flag curvature and constant S-curvature must be Riemannian if the manifold is compact. We also study the nonpositive flag curvature case.supported by the National Natural Science Foundation of China (10371138). 相似文献
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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
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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
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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.
14.
Xiaohuan Mo Newton Mayer Solórzano Keti Tenenblat 《Differential Geometry and its Applications》2013,31(6):746-758
We obtain the differential equation that characterizes the spherically symmetric Finsler metrics with vanishing Douglas curvature. By solving this equation, we obtain all the spherically symmetric Douglas metrics. Many explicit examples are included. 相似文献
15.
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
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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
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Square metrics is an important class of Finsler metrics. Recently, we introduced a special class of non-regular Finsler metrics called singular square metrics. The main purpose of this paper is to provide a necessary and sufficient condition for singular square metrics to be of constant Ricci or flag curvature when dimension . 相似文献
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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
19.
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
20.
XIAOHUAN MO 《Proceedings Mathematical Sciences》2012,122(3):411-427
By finding Killing vector fields of general Bryant??s metric we give a lot of new Finsler metrics of constant (or scalar) flag curvature and determine their scalar curvature. 相似文献