On the Tangent Bundle of a Hypersurface in a Riemannian Manifold

On the Tangent Bundle of a Hypersurface in a Riemannian Manifold

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摘要 Let （Mn, g） and （N^n＋1, G） be Riemannian manifolds. Let TMn and TN^n＋1 be the associated tangent bundles. Let f ：（M^n, g） → （N^＋1, G） be an isometrical immersion with g = f^＊G, F = （f, df）：（TM^n,g） → （TN^n＋1, Gs） be the isometrical immersion with g= F＊Gs 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 TM^n as a submanifold of TN^n＋1 by the moving frame method. The authors firstly study the extrinsic geometry of TMn in TN^n＋1. Then the integrability of the induced almost complex structure of TM is discussed.

作者 Zhonghua HOU Lei SUN

机构地区 Institute of Mathematics Department of Mathematics

出处《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2015年第4期579-602,共24页 数学年刊（B辑英文版）

基金 supported by the National Natural Science Foundation of China(No.61473059) the Fundamental Research Funds for the Central University(No.DUT11LK47)

关键词 HYPERSURFACES Tangent bundle Mean curvature vector Sasaki metric Almost complex structure Kghlerian form Riemann曲面子流形切丛等距浸入几何形状 TMN 活动标架法近复结构

分类号 O186.12 [理学—基础数学]

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Chinese Annals of Mathematics,Series B

2015年第4期

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On the Tangent Bundle of a Hypersurface in a Riemannian Manifold

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