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On hypersurfaces with two distinct principal curvatures in a unit sphere
Authors:Bing Ye Wu  
Institution:aDepartment of Mathematics, Minjiang University, Fuzhou, Fujiang 350108, China
Abstract:We investigate the immersed hypersurfaces in a unit sphere View the MathML source. By using Otsuki's idea, we obtain the local and global classification results for immersed hypersurfaces in View the MathML source of constant m-th mean curvature and two distinct principal curvatures of multiplicities n−1,1 (in the local version, we assume that the principal curvatures are non-zero when mgreater-or-equal, slanted2). As the result, we prove that any local hypersurface in View the MathML source of constant mean curvature and two distinct principal curvatures is an open part of a complete hypersurface of the same curvature properties. The corresponding result does not hold for m-th mean curvature when mgreater-or-equal, slanted2.
Keywords:Hypersurface  Principal curvature  Mean curvature
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