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1.
本文研究了Finsler流形中的子流形,特别地,我们给出了闵可夫斯基空间中超球面的一个特征,同时,我们讨论了闵可夫斯基空间中超曲面的第二基本形式。 相似文献
2.
本文利用Finsler约度量函数与度量张量获得了二维Finsler空间是共形平坦的若干令新的充要条件.此外,还推导了在共形映射下,局部Minkowski空间、常曲率Finsler空间与零曲率Finsler空间保持不变的新的充要条件. 相似文献
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For a Euclidean space or a Minkowski space, we change the metric in a compact subset and show that the resulting Finsler manifold is isometric to the original standard space under certain conditions. We assume that the mean tangent curvature vanishes and the metric satisfies some curvature conditions or have no conjugate points. 相似文献
5.
Parastoo Habibi Dariush Latifi Megerdich Toomanian 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2011,46(1):12-16
In this paperwe study the set of homogeneous geodesics of a left-invariant Finsler metric on Lie groups. We first give a simple criterion that characterizes geodesic vectors. We extend J. Szenthe’s result on homogeneous geodesics to left-invariant Finsler metrics. This result gives a relation between geodesic vectors and restricted Minkowski norm in Finsler setting. We show that if a compact connected and semisimple Lie group has rank greater than 1, then for every left-invariant Finsler metric there are infinitely many homogeneous geodesics through the identity element. 相似文献
6.
In this paper, we introduce the notion of a Minkowski Lie algebra, which is the natural generalization of the notion of a
real quadratic Lie algebra (metric Lie algebra). We then study the positive definite Minkowski Lie algebras and obtain a complete
classification of the simple ones. Finally, we present some applications of our results to Finsler geometry and give a classification
of bi-invariant Finsler metrics on Lie groups.
This work was supported by NSFC (No.10671096) and NCET of China. 相似文献
7.
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
8.
首先利用中心仿射几何中的结果建立了Minkowski空间的等价性定理.作为在Finsler几何中的应用,我们证明满足一定条件的Landsberg空间为Berwald空间,这些条件可以是具有闭的Cartan型形式,S曲率为零或平均Berwald曲率为零. 相似文献
9.
吴炳烨 《数学年刊A辑(中文版)》2006,(1)
本文对一般的Finsler体积元讨论了Finsler子流形几何,证明了关于任意Finsler体积元, Minkowski空间中不存在闭定向的极小子流形,关键在于对任意的Finsler体积元,沈忠民的方法仍然有效.对于特殊Randers空间中的子流形,给出了其体积增长估计,从而得到了Randers空间可以极小浸入到特殊Randers空间的一个必要条件. 相似文献
10.
The conformai theory of Finsler spaces was initiated by Knebelman in 1929 and lately Kikuchi [7] gave the conditions for a
Finsler space to be conformai to a Minkowski space. However under theh-condition, the third author [4] obtained the conditions for a Finsler space to beh-conformal to a Minkowski space.
The purpose of the paper is to investigate the infinitesimalh-conformal motions of Finsler metric and its application to anH-recurrent Finsler space. We obtain the following results.
A. | Theorem 2.1. If an HR-F n space is a Landsberg space, then the tensorF hjk i is recurrent. | |
B. |
Proposition 3.3. An infinitesimalh-conformal motion satisfies
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