The Pinching Theorem of Global Umbilic Submanifolds in a Riemannian Manifold with Quasi Constant Curvature

Chinese Quarterly Journal of Mathematics ›› 2006, Vol. 21 ›› Issue (3): 342-350.

The Pinching Theorem of Global Umbilic Submanifolds in a Riemannian Manifold with Quasi Constant Curvature

Department of Mathematics, East China Normal University, Shanghai 200062, China; Department of Mathematics, Nantong University, Nantong 226007, China

Received:2004-02-09 Online:2006-09-30 Published:2023-11-27
About author:WANG Lin-feng(1973-),male,native of Nantong,Jiangsu,a lecturer of Nantong University,en- gages in the theory of submanifolds.
Supported by:
Supported by the Directing Research Subject of Jiangsu Education Bureau(03103146)；

Abstract

Abstract: We study the global umbilic submanifolds with parallel mean curvature vector fields in a Riemannian manifold with quasi constant curvature and get a local pinching theorem about the length of the second fundamental form.

Key words: constant , , curvature, parallel , , mean , , curvature , , vector , , fields, global , , umbilic points, globally geodesic submanifolds

CLC Number:

O186.12

WANG Lin-feng . The Pinching Theorem of Global Umbilic Submanifolds in a Riemannian Manifold with Quasi Constant Curvature[J]. Chinese Quarterly Journal of Mathematics, 2006, 21(3): 342-350.

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The Pinching Theorem of Global Umbilic Submanifolds in a Riemannian Manifold with Quasi Constant Curvature

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