Abstract
In this paper, the rigidity theorems of the submanifolds in Sn+p with parallel Möbius form and constant Möbius scalar curvature are given.
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Chern S S, do Carmo M, Kobayashi S. Minimal submanifolds of a shpere with second fundemantal form of constant length. Chern Shengshen selected papers, Vol. I, Berlin-Heideberg-New York, 1978, 393–409.
Cecil T E, Ryan P J. Tight and taut immersions of manifolds, Research Notes in Mathematies 107, Pitman Advanced Publishing Program, 1985.
Hu Z J, Li H Z. Submanifolds with constant Möbius scalar curvature in Sn, Manuscripta Math, 2003,111:287–302.
Li A M, Li J M. An intrinsic rigidity theorm for minimal submanifolds in a sphere, Arch Math, 1992,58:582–594.
Li H Z, Liu H L, Wang C P, et al. Möbius isoparametric hypersurfaces in Sn+1 with two distinct principal curvatures, Acta Mathematica Sinica, English Series, 2002,18(3):437–446.
Liu H L, Wang C P, Zhao G S. Möbius isotropic submanifolds in Sn, Tohoku Math J, 2001,53:553–569.
Santos W. Submanifolds with parallel mean curvature vector in spheres, Tohoku Math J, 1994,46:403–415.
Wang C P. Möbius geometry of submanifolds in Sn, Manuscripta Math, 1998,96:517–533.
Zhong D X. A formula for submanifolds in Sn and its applications in Möbius geometry, Northeast Math J(China), 2001,17(3):361–370.
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Supported by the National Natural Science Foundation of China (10271106), the Natural Science Foundation of Zhejiang Province (M103047) and the Education Department of Zhejiang Province (20030342).
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Qiaoling, X. Submanifolds in Sn+p with parallel Möbius from. Appl. Math. Chin. Univ. 19, 405–416 (2004). https://doi.org/10.1007/s11766-004-0007-z
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DOI: https://doi.org/10.1007/s11766-004-0007-z