| 关于切丛和单位切球丛的度量的一个注记 |
| |
| 引用本文： | 李兴校,齐学荣. 关于切丛和单位切球丛的度量的一个注记[J]. 数学研究及应用, 2008, 28(4): 829-838 |
| |
| 作者姓名： | 李兴校 齐学荣 |
| |
| 作者单位： | 河南师范大学数学学院. 河南 新乡 453007;河南师范大学数学学院. 河南 新乡 453007 |
| |
| 基金项目： | 国家自然科学基金(No.10671181). |
| |
| 摘 要： | 本文在黎曼流形$(M,g)$的切丛$TM$ 上研究与参考文献[10]中平行的一类度量$G$以及相容的近复结构$J$.证明了切丛$TM$关于这些度量和相应的近复结构是局部共形近K"{a}hler流形,并且把这些结构限制在单位切球丛上得到了切触度量结构的新例子.
|
| 关 键 词： | 局部共形近K" {a}hler流形 Vaisman流形 切触度量结构 Sasakian流形. |
| 收稿时间： | 2006-09-18 |
| 修稿时间： | 2007-07-13 |
A Note on Some Metrics on Tangent Bundles and Unit Tangent Sphere Bundles |
| |
| LI Xing Xiao and QI Xue Rong. A Note on Some Metrics on Tangent Bundles and Unit Tangent Sphere Bundles[J]. Journal of Mathematical Research with Applications, 2008, 28(4): 829-838 |
| |
| Authors: | LI Xing Xiao and QI Xue Rong |
| |
| Affiliation: | Department of Mathematics, Henan Normal University, Henan 453007, China;Department of Mathematics, Henan Normal University, Henan 453007, China |
| |
| Abstract: | In this paper we study a class of metrics with some compatible almost complex structures on the tangent bundle $TM$ of a Riemannian manifold $(M,g)$, which are parallel to those in [10]. These metrics generalize the classical Sasaki metric and Cheeger-Gromoll metric. We prove that the tangent bundle $TM$ endowed with each pair of the above metrics and the corresponding almost complex structures is a locally conformal almost kr manifold. We also find that, when restricted to the unit tangent sphere bundle, these metrics and corresponding almost complex structures define new examples of contact metric structures. |
| |
| Keywords: | locally conformal almost K" ahler manifold Vaisman manifold contact metric structure Sasakian manifold. |
|
| 点击此处可从《数学研究及应用》浏览原始摘要信息 |
|
点击此处可从《数学研究及应用》下载全文 |
