共查询到20条相似文献,搜索用时 15 毫秒
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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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In this paper, we study locally projectively flat Finsler metrics with constant flag curvature K. We prove those are totally determined by their behaviors at the origin by solving some nonlinear PDEs. The classifications when K=0, K=−1 and K=1 are given respectively in an algebraic way. Further, we construct a new projectively flat Finsler metric with flag curvature K=1 determined by a Minkowski norm with double square roots at the origin. As an application of our main theorems, we give the classification of locally projectively flat spherical symmetric Finsler metrics much easier than before. 相似文献
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In this paper, we classify locally projectively flat general -metrics on an -dimensional manifold if α is of constant sectional curvature and . Furthermore, we find equations to characterize this class of metrics with constant flag curvature and determine their local structures. 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
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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
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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
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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
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Some constructions of projectively flat Finsler metrics 总被引:6,自引:0,他引:6
MO Xiaohuan SHEN Zhongmin & YANG Chunhong LMAM School of Mathematical Sciences Peking University Beijing China Department of Mathematical Sciences Indiana University-Purdue University Indianapolis IN - USA Department of Mathematics Inner Mongolia University Hohhot China 《中国科学A辑(英文版)》2006,49(5):703-714
In this paper, we find some solutions to a system of partial differential equations that characterize the projectively flat Finsler metrics. Further, we discover that some of these metrics actually have the zero flag curvature. 相似文献
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We show that in dimension 2 every Finsler metric with at least 3-dimensional Lie algebra of projective vector fields is locally projectively equivalent to a Randers metric. We give a short list of such Finsler metrics which is complete up to coordinate change and projective equivalence. 相似文献
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The Weyl curvature is one of the fundamental quantities in Finsler geometry because it is a projective invariant. By determining the Weyl curvature of a class of Finsler metrics, we find a lot of Finsler metrics of quadratic Weyl curvature which are non-trivial in the sense that they are not of quadratic Riemann curvature. 相似文献
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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
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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
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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