Hou, Zhong Hua
Professor Supervisor of Doctorate Candidates Supervisor of Master's Candidates
Gender:Male
Alma Mater:日本东京工业大学
Degree:Doctoral Degree
School/Department:数学科学学院
Discipline:Pure Mathematics
E-Mail:zhonghua@dlut.edu.cn
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Indexed by:Journal Papers
Date of Publication:2015-07-01
Journal:CHINESE ANNALS OF MATHEMATICS SERIES B
Included Journals:SCIE、ISTIC、CSCD、Scopus
Volume:36
Issue:4
Page Number:579-602
ISSN No.:0252-9599
Key Words:Hypersurfaces; Tangent bundle; Mean curvature vector; Sasaki metric; Almost complex structure; Kahlerian form
Abstract:Let (M-n, g) and (Nn+1, G) be Riemannian manifolds. Let TMn and TNn+1 be the associated tangent bundles. Let f : (M-n, g) -> (Nn+1, G) be an isometrical immersion with g = f* G, F = (f, df) : (T M-n, (g) over bar) -> (TNn+1, G(s)) be the isometrical immersion with (g) over bar = F* G(s) where (df)(x) : TxM -> T-f(x) N for any x is an element of 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.
