首页 | 本学科首页   官方微博 | 高级检索  
     检索      


On the Tangent Bundle of a Hypersurface in a Riemannian Manifold
Authors:Zhonghua HOU and Lei SUN
Abstract:Let $(M^n,g)$ and $(N^{n+1},G)$ be Riemannian manifolds. Let $TM^n$ and $TN^{n+1}$ be the associated tangent bundles. Let $f: (M^n,g) \to (N^{n+1},G)$ be an isometrical immersion with $g=f^\ast G$, $F=(f, df): (TM^n,\ov {g}) \to (TN^{n+1},G_s)$ be the isometrical immersion with $\ov {g}=F^\ast G_s$ where $(df)_x: T_xM\to T_{f(x)}N$ for any $x\in M$ is the differential map, and $G_s$ be the Sasaki metric on $TN$ induced from $G$. This paper deals with the geometry of $TM^n$ as a submanifold of $TN^{n+1}$ by the moving frame method. The authors firstly study the extrinsic geometry of $TM^n$ in $TN^{n+1}$. Then the integrability of the induced almost complex structure of $TM$ is discussed.
Keywords:
本文献已被 CNKI 万方数据 等数据库收录!
点击此处可从《数学年刊B辑(英文版)》浏览原始摘要信息
点击此处可从《数学年刊B辑(英文版)》下载免费的PDF全文
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号