| 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 |
| 关于切丛和单位切球丛的度量的一个注记 |
| A Note on Some Metrics on Tangent Bundles and Unit Tangent Sphere Bundles |
| 投稿时间：2006-09-18 修订日期：2007-07-13 |
| DOI：10.3770/j.issn:1000-341X.2008.04.011 |
| 中文关键词: 局部共形近K\"{a}hler流形 Vaisman流形 切触度量结构 Sasakian流形. |
| 英文关键词:locally conformal almost K\"ahler manifold Vaisman manifold contact metric structure Sasakian manifold. |
| 基金项目:国家自然科学基金(No.10671181). |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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. |
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