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http://dx.doi.org/10.4134/BKMS.2012.49.2.285

HYPERSURFACES WITH CONSTANT k-TH MEAN CURVATURE AND TWO DISTINCT PRINCIPAL CURVATURES IN SPHERES  

Liu, Jiancheng (College of Mathematics and Information Science Northwest Normal University)
Wei, Yan (College of Mathematics and Information Science Northwest Normal University)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.2, 2012 , pp. 285-293 More about this Journal
Abstract
In this paper, we investigate the hypersurface M in a unit sphere with constant k-th mean curvature and two distinct principal curvatures, and characterize such a hypersurface.
Keywords
sphere; hypersurface; k-th mean curvature; principal curvatures; Riemannian product space;
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1 S. S. Chern, M. do Carmo, and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, In Functional Analysis and Related Fields, pp. 59-75, Springer, 1970.
2 Jr. H. B. Lawson, Local rigidity theorems for minimal hypersurfaces, Ann. of Math. (2) 89 (1969), 167-179.
3 H. Li, Global rigidity theorems of hypersurfaces, Ark. Mat. 35 (1997), no. 2, 327-351.   DOI   ScienceOn
4 T. Otsuki, Minimal hypersurfaces in a Riemannian manifold of constant curvature, Amer. J. Math. 92 (1970), 145-173.   DOI   ScienceOn
5 G. Wei, Complete hypersurfaces with constant mean curvature in a unit sphere, Monatsh. Math. 149 (2006), no. 3, 251-258.   DOI   ScienceOn
6 G. Wei, Rigidity theorems of hypersurfaces with constant scalar curvature in a unit sphere, Acta Math. Sin. (Engl. Ser.) 23 (2007), no. 6, 1075-1082.   DOI   ScienceOn
7 G. Wei, Complete hypersurfaces with $H_{\kappa}$ = 0 in a unit sphere, Differential Geom. Appl. 25 (2007), no. 5, 500-505.   DOI   ScienceOn
8 E. Cartan, Familles de surfaces isoparametriques dans les espaces a courvure constante, Ann. Mat. Pura Appl. 17 (1938), no. 1, 177-191.   DOI   ScienceOn
9 H. Alencar and M. do Carmo, Hypersurfaces with constant mean curvature in spheres, Proc. Amer. Math. Soc. 120 (1994), no. 4, 1223-1229.   DOI   ScienceOn
10 J. N. Barbosa, Hypersurfaces of $S^{n+1}$ with two distinct principal curvatures, Glasg. Math. J. 47 (2005), no. 1, 149-153.   DOI   ScienceOn
11 Q. M. Cheng, Hypersurfaces in a unit sphere $S^{n+1}$(1) with constant scalar curvature, J. London Math. Soc. (2) 64 (2001), no. 3, 755-768.   DOI
12 Q. M. Cheng and S. Ishikawa, A characterization of the Clifford torus, Proc. Amer. Math. Soc. 127 (1999), no. 3, 819-828.   DOI   ScienceOn
13 S. Y. Cheng and S. T. Yau, Hypersurfaces with constant scalar curvature, Math. Ann. 225 (1977), no. 3, 195-204.   DOI   ScienceOn