Bulletin of the Australian Mathematical Society
- Bulletin of the Australian Mathematical Society / Volume 44 / Issue 03 / December 1991, pp 391-396
- Copyright © Australian Mathematical Society 1991
- DOI: http://dx.doi.org/10.1017/S0004972700029890 (About DOI), Published online: 17 April 2009
Research Article
Finite type pseudo-umbilical submanifolds in a hypersphere
Shi-Jie Lia1
a1 Department of Mathematics, South China Normal University Guangzhou, China
Abstract
The notion of finite type submanifolds was introduced by B.Y. Chen. In this article we study 2- and 3-type pseudo-umbilical submanifolds in a hypersphere. Two theorems in this respect are obtained.
(Received November 26 1990)
- [1] Chen, B.Y., Total mean curvature and submanifolds of finite type (World Scientific, Singapore, New Jersey, London, Hong Kong, 1984). [Google Scholar]
- [2] Chen, B.Y., ‘2-type submanifolds and their applications’, Chinese J. Math. 14 (1986), 1–14. [OpenURL Query Data] [Google Scholar]
- [3] Chen, B.Y., Barros, M. and Garay, O.J., ‘Spherical finite type hypersurfaces’, Algebras. Groups and Geometries 4 (1987), 58–72. [OpenURL Query Data] [Google Scholar]
- [4] Garay, O.J., ‘Spherical Chen surfaces which are mass-symmetric and of 2-type’, J. Geom. 33 (1988), 39–52. [OpenURL Query Data] [CrossRef] [Google Scholar]
- [5] Li, S.J., ‘2-type pseudo-umbilical submanifolds’, Bull. Soc. Math. Belg. Ser. B 43 (1991), 69–74. [OpenURL Query Data] [Google Scholar]
- [6] Takahashi, T., ‘Minimal immersions of Riemannian manifolds’, J. Math. Soc. Japan 18 (1966), 380–385. [OpenURL Query Data] [CrossRef] [Google Scholar]
