Biharmonic hypersurfaces with three distinct principal curvatures in spheres |
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Authors: | Yu Fu |
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Institution: | 1. School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Dalian, P. 2. R. 3. China |
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Abstract: | We obtain a complete classification of proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces with arbitrary dimension. Precisely, together with known results of Balmu?‐Montaldo‐Oniciuc, we prove that compact orientable proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces are either the hypersphere or the Clifford hypersurface with and . Moreover, we also show that there does not exist proper biharmonic hypersurface with at most three distinct principal curvatures in hyperbolic spaces . |
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Keywords: | Biharmonic submanifolds principal curvatures generalized Chen's conjecture 53C40 53C42 53D12 |
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