On fiberings of almost contact manifolds
On fiberings of almost contact manifolds
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几乎接触式管汇的纤维化
DOI：
10.2996/kmj/1138845019
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发表时间：
1965
期刊：
影响因子：
--
通讯作者：
K. Ogiue
中科院分区：
文献类型：
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作者：
K. Ogiue
本文研究了几乎切触结构与诱导复结构之间的关系。在本文中，我们考虑几乎切触流形M是几乎复流形M上的主纤维丛的丛空间的情形。在§1中，我们导出了M上的一个几乎复结构。在§ 2中，我们分别考虑了Nijenhuis [4]和Sasaki-Hatakeyama [8]定义的几乎切触结构的两类挠率N和Φ，并研究了M上诱导的几乎复结构的可积性与TV或Φ的消失之间的关系。在§3中，我们考虑了M上的几乎切触度量结构，导出了M上的几乎厄米特结构，并研究了它们之间的关系。在§4中，我们作为特例研究了M上的几乎Sasaki结构和Sasaki结构，并导出了M上的几乎Kahler结构和Kahler结构。最后一节研究了M上的黎曼联络与M上的黎曼联络之间的关系以及M的曲率与M的曲率之间的关系。在此，我衷心感谢K教授。Yano和S.石原先生鼓励我研究这些问题，并给了我许多宝贵的建议。
We study, in this paper, relations between almost contact structures and the induced complex structures. Throughout this paper, we consider the case in which an almost contact manifold M is the bundle space of a principal fibre bundle over an almost complex manifold M. We induce, in §1, an almost complex structure on M. We consider, in § 2, two sorts of torsions N and Φ of an almost contact structure defined by Nijenhuis [4] and Sasaki-Hatakeyama [8] respectively, and investigate relations between the integrability of the induced almost complex structure on M and the vanishing of TV or Φ. In §3 we consider an almost contact metric structure on M and induce an almost Hermitian structure on M and investigate relations between them. In §4 we study, as special cases, an almost Sasakian structure and a Sasakian structure on M and induce on M an almost Kahler structure and a Kahler structure. In the last section we study a relation between the Riemannian connection on M and on M and a relation between the curvature of M and the curvature of M. I wish to express my sincere gratitude to Professors K. Yano and S. Ishihara who encouraged me to study these problems and gave many valuable suggestions.