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EMBEDDED HYPERSURFACES WITH CONSTANT mTH MEAN CURVATURE IN A UNIT SPHERE
2010
Communications in Contemporary Mathematics
In this paper, we study n-dimensional hypersurfaces with constant mth mean curvature in a unit sphere S n+1 (1) and construct many compact nontrivial embedded hypersurfaces with constant mth mean curvature Hm > 0 in S n+1 (1), for 1 ≤ m ≤ n − 1. Moreover, if the 2nd mean curvature H 2 takes value between 1 (tan π k ) 2 and k 2 −2 n for any integer k ≥ 2 and n ≥ 3, then there exists an n-dimensional compact nontrivial embedded hypersurface with constant H 2 (i.e. constant scalar curvature) in S
doi:10.1142/s0219199710004081
fatcat:vk3e7q5ro5ethaytosrzmyxm6y