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1.
On Douglas general (<Emphasis Type="Italic">α</Emphasis>, <Emphasis Type="Italic">β</Emphasis>)-metrics 下载免费PDF全文
Douglas metrics are metrics with vanishing Douglas curvature which is an important projective invariant in Finsler geometry. To find more Douglas metrics, in this paper we consider a class of Finsler metrics called general (α, β)-metrics, which are defined by a Riemannian metric \(\alpha = \sqrt {{a_{ij}}\left( x \right){y^i}{y^j}} \) and a 1-form β = b i (x)y i . We obtain the differential equations that characterizes these metrics with vanishing Douglas curvature. By solving the equivalent PDEs, the metrics in this class are totally determined. Then many new Douglas metrics are constructed. 相似文献
2.
We study a class of Finsler metrics which contains the class of P-reducible metrics. Finsler metrics in this class are called generalized P-reducible metrics. We consider generalized P-reducible metrics with scalar flag curvature and find a condition under which these metrics reduce to C-reducible metrics. This generalizes Matsumoto’s theorem, which describes the equivalency of C-reducibility and P-reducibility on Finsler manifolds with scalar curvature. Then we show that generalized P-reducible metrics with vanishing stretch curvature are C-reducible. 相似文献
3.
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
4.
In this paper we extend the results on projective changes of complex Finsler metrics obtained in Aldea and Munteanu (2012) [3], by the study of projective curvature invariants of a complex Finsler space. By means of these invariants, the notion of complex Douglas space is then defined. A special approach is devoted to the obtaining of equivalence conditions for a complex Finsler space to be a Douglas one. It is shown that any weakly Kähler Douglas space is a complex Berwald space. A projective curvature invariant of Weyl type characterizes complex Berwald spaces. These must be either purely Hermitian of constant holomorphic curvature, or non-purely Hermitian of vanishing holomorphic curvature. Locally projectively flat complex Finsler metrics are also studied. 相似文献
5.
《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
6.
Periodica Mathematica Hungarica - In this paper, we define a weaker notion of Douglas metrics, namely weakly Douglas metrics. A Finsler metric satisfies a projectively invariant equation... 相似文献
7.
朱红梅 《数学物理学报(B辑英文版)》2018,38(2):695-708
In this article, we study a class of Finsler metrics called general(α, β)-metrics,which are defined by a Riemannian metric α and a 1-form β. We determine all of Douglas general(α, β)-metrics on a manifold of dimension n 2. 相似文献
8.
本文得到Matsumoto度量具有可反Douglas曲率的充分必要条件,该条件蕴含存在具有可反Douglas曲率的非Douglas的Finsler度量. 相似文献
9.
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
10.
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
11.
In this paper, we consider some generalization of maximally movable spaces of Finsler type. Among them, there are locally
conic spaces (Riemannian metrics of their tangent spaces are realized on circular cones) and generalized Lagrange spaces with
Tamm metrics (their tangent Riemannian spaces admit all rotations). On the tangent bundle of a Riemannian manifold, we study
a special class of almost product metrics, generated Tamm metric. This class contains Sasaki metric and Cheeger–Gromol metric.
We determine the position of this class in the Naveira classification of Riemannian almost product metrics. 相似文献
12.
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
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.
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
15.
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
16.
In this paper, we study generalized Douglas–Weyl(α, β)-metrics. Suppose that a regular(α, β)-metric F is not of Randers type. We prove that F is a generalized Douglas–Weyl metric with vanishing S-curvature if and only if it is a Berwald metric. Moreover, by ignoring the regularity, if F is not a Berwald metric, then we find a family of almost regular Finsler metrics which is not Douglas nor Weyl. As its application, we show that generalized Douglas–Weyl square metric or Matsumoto metric with isotropic mean Berwald curvature are Berwald metrics. 相似文献
17.
In this paper, we discuss a class of Finsler metrics defined by a Riemannian metric and a 1-form on a manifold. We characterize weak Landsberg metrics in this class and show that there exist weak Landsberg metrics which are not Landsberg metrics in dimension greater than two. 相似文献
18.
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
19.
S. V. Ivanov 《Proceedings of the Steklov Institute of Mathematics》2011,273(1):176-190
We prove that every Riemannian metric on the 2-disc such that all its geodesics are minimal is a minimal filling of its boundary
(within the class of fillings homeomorphic to the disc). This improves an earlier result of the author by removing the assumption
that the boundary is convex. More generally, we prove this result for Finsler metrics with area defined as the two-dimensional
Holmes-Thompson volume. This implies a generalization of Pu’s isosystolic inequality to Finsler metrics, both for the Holmes-Thompson
and Busemann definitions of the Finsler area. 相似文献
20.
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