On hypersurfaces with two distinct principal curvatures in a unit sphere |
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Authors: | Bing Ye Wu |
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Institution: | aDepartment of Mathematics, Minjiang University, Fuzhou, Fujiang 350108, China |
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Abstract: | We investigate the immersed hypersurfaces in a unit sphere . By using Otsuki's idea, we obtain the local and global classification results for immersed hypersurfaces in 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 m 2). As the result, we prove that any local hypersurface in 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 m 2. |
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Keywords: | Hypersurface Principal curvature Mean curvature |
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