On hypersurfaces with two distinct principal curvatures in space forms |
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Authors: | BING YE WU |
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Institution: | 1.Department of Mathematics,Minjiang University,Fuzhou,China |
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Abstract: | We investigate the immersed hypersurfaces in space forms ℕ
n + 1(c), n ≥ 4 with two distinct non-simple principal curvatures without the assumption that the (high order) mean curvature is constant.
We prove that any immersed hypersurface in space forms with two distinct non-simple principal curvatures is locally conformal
to the Riemannian product of two constant curved manifolds. We also obtain some characterizations for the Clifford hypersurfaces
in terms of the trace free part of the second fundamental form. |
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Keywords: | |
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