期刊文献+

具有迷向S曲率Randers度量的几何意义(英文) 被引量:2

The Geometric Meaning of Randers Metrics With Isotropic S-curvature
下载PDF
导出
摘要 Riemann流形上的Zermelo航行为Randers度量提供了一个简洁而且清晰的几何背景.在这个背景下D.Bao,C.Robles和Z.Shen对于具有常旗曲率的Randers度量进行了完全分类.这篇论文中,我得到了判定具有特殊曲率性质的Randers度量的两个充分必要条件.从这两个条件出发,我得到了迷向S曲率的Randers度量的几何意义和一系列推论,并且构造了具有迷向S曲率Randers度量的新例子.最后,在Zermelo航行的背景下研究了Berwald型的Randers度量. The Zermelo navigation on Riemannian manifolds provides a succinct and geometric description of Randers metrics. With this description, D. Bao, C. Robles and Z. Shen have completely classified Randers metrics of constant flag curvature. In this paper, I study Randers metrics under the navigation description and discover two sufficient and necessary conditions for Randers metrics of special curvature properties, which are more geometrically meaningful than the traditional description. And several propositions and examples resulted from these conditions are included. Furthermore, I investigate thoroughly with Randers metrics of Berwald type under the navigation description.
作者 邢浩
出处 《数学进展》 CSCD 北大核心 2005年第6期717-730,共14页 Advances in Mathematics(China)
基金 Research supported in part by Beijing University President Foundation.
关键词 FINSLER流形 RANDERS度量 S曲率 Finsler manifold Randers metric S-curvature
  • 引文网络
  • 相关文献

参考文献11

  • 1An Introduction to Riemann-Finsler Geometry [M]. Graduate Texts in Mathematics, vol.200, Springer. 被引量:1
  • 2Bao D, Robles C, Shen Z. Zermelo navigation on Riemannian manifolds [C]. preprint, 2003. 被引量:1
  • 3Chen X, Shen Z. Randers metrics with special curvature properties [J]. Osaka J. Math., 2003, 40: 87-101. 被引量:1
  • 4Matsumoto M. On Finsler spaces with Randers metric and special forms of important tensors [J]. J. Math.Koyoto Univ., 1974, 14: 477-498. 被引量:1
  • 5Randers G. On an asymmetric metric in the four-spaces of general relativity [J]. Phys. Rev., 1941, 59:195-199. 被引量:1
  • 6Shen Z. Lectures on Finsler Geometry [M]. World Scientific, Singapore: 2001. 被引量:1
  • 7Shen Z. Two-dimensional Finsler metrics of constant curvature [J]. Manuscripta Mathematica, 2002, 109:349-366. 被引量:1
  • 8Shen Z. Finsler metircs with K = 0 and S = 0 [J]. Canadian J. Math., 2003, 55: 112-132. 被引量:1
  • 9Shen Z. Projectively flat Randers metrics with constant flag curvature [J]. Math. Ann., 2003, 325: 19-30. 被引量:1
  • 10Shibata C, Shimada H, Azuma M, Yasuda H. On Finsler spaces with Randers metric [J]. Tensor, N. S., 1977,31: 219-226. 被引量:1

同被引文献2

引证文献2

二级引证文献11

相关主题

;
使用帮助 返回顶部