CLC number: O186

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Received: 2004-06-06

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ZHANG Jian-feng. A rigidity theorem for submanifolds in *S ^{n}*

@article{title="A rigidity theorem for submanifolds in *S ^{n}*

author="ZHANG Jian-feng",

journal="Journal of Zhejiang University Science A",

volume="6",

number="4",

pages="322~328",

year="2005",

publisher="Zhejiang University Press & Springer",

doi="10.1631/jzus.2005.A0322"

}

%0 Journal Article

%T A rigidity theorem for submanifolds in *S ^{n}*

%A ZHANG Jian-feng

%J Journal of Zhejiang University SCIENCE A

%V 6

%N 4

%P 322~328

%@ 1673-565X

%D 2005

%I Zhejiang University Press & Springer

%DOI 10.1631/jzus.2005.A0322

TY - JOUR

T1 - A rigidity theorem for submanifolds in *S ^{n}*

A1 - ZHANG Jian-feng

J0 - Journal of Zhejiang University Science A

VL - 6

IS - 4

SP - 322

EP - 328

%@ 1673-565X

Y1 - 2005

PB - Zhejiang University Press & Springer

ER -

DOI - 10.1631/jzus.2005.A0322

**Abstract: **Let

**
**

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[3] Chern, S.S., de Carmo, M., Kobayashi, S., 1970. Minimal Submanifolds of A Sphere with Second Fundamental Form of Constant Length. Functional A Analysis and Related Fields, p.59-75.

[4] Hou, Z.H., 1997. Hypersurfaces in sphere with constant mean curvature. *Proc Amer Soc*, **125**(4):1193-1196.

[5] Hou, Z.H., 1998. Submanifolds of constant scalar curvature in a space form. *Kyun Math J*, **38**:439-458.

[6] Li, A.M., Li, J.M, 1992. An intrinsic rigidity theorem for minimal submanifolds in a sphere. *Arch Math*, **58**:582-594.

[7] Li, H.Z., 1994. Hypersurfaces with parallel mean curvature in a space forms. *Math Ann*, **305**:403-415.

[8] Okumura, M., 1974. Hypersurfaces and a pinching problem on the second fundamental tensor. *Amer J Math*, **96**:207-213.

[9] Simons, J., 1968. Minimal varieties in Riemannian manifolds. *Ann of Math*, **88**(2):62-105.

[10] Zhang, J.F., 1999. On submanifolds with parallel mean curvature vector in a locally symmetric conformally flat riemannian manifold. *J Zhejiang Univ (Engineering Science)*, **26**(4):26-34 (in Chinese).

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