On the tangent bundle of a hypersurface in a Riemannian manifold

被引：0
作者：
Zhonghua Hou
Lei Sun
机构：
[1] Dalian University of Technology,Institute of Mathematics
[2] Northeast Forestry University,Department of Mathematics
来源：
Chinese Annals of Mathematics, Series B | 2015年 / 36卷
关键词：
Hypersurfaces; Tangent bundle; Mean curvature vector; Sasaki metric; Almost complex structure; Kählerian form; 32Q60; 53C42;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let (Mn, g) and (Nn+1, G) be Riemannian manifolds. Let TMn and TNn+1 be the associated tangent bundles. Let f: (Mn, g) → (Nn+1,G) be an isometrical immersion with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g = f*G,F = (f,df):(TM^n ,\bar g) \to (TN^{n + 1} ,G_s )$$\end{document} be the isometrical immersion with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar g = F*G_s$$\end{document} where (df)x: TxM → Tf(x)N for any x ∈ M is the differential map, and Gs be the Sasaki metric on TN induced from G. This paper deals with the geometry of TMn as a submanifold of TNn+1 by the moving frame method. The authors firstly study the extrinsic geometry of TMn in TNn+1. Then the integrability of the induced almost complex structure of TM is discussed.
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页码：579 / 602
页数：23
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