Submanifolds with Parallel Normalized Mean Curvature Vector in a Sphere
Received:June 28, 2000  
Key Words: sphere   mean curvature   normalized mean curvature vector.  
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Author NameAffiliation
WANG Mei-jiao Dept. of Math.
Guangzhou University
Guangdong
China 
LI Shi-jie Dept. of Math.
South China Normal University
Guangzhou
China 
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Abstract:
      Let M be a closed n-dimensional Riemannian manifold immersed in a unit sphere Sn+p,p≥2 , with parallel normalized mean curvature vector. Denote by 5 the square of the length of the second fundamental form of M. It is proved that if S ≤min{2n/3, 2(n-1)1/2}, then M is a hypersurface of a (n +1)-dimensional totally geodesic submanifold Sn+1 of Sn+p. This improve a result of Mo Xiaohuan.
Citation:
DOI:10.3770/j.issn:1000-341X.2003.03.024
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