Biharmonic Hypersurfaces in Es5

Yu FU, Zhong Hua HOU, Dan YANG, Xin ZHAN

Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (2) : 335-352.

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Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (2) : 335-352. DOI: 10.12386/A2022sxxb0027

Biharmonic Hypersurfaces in Es5

  • Yu FU1, Zhong Hua HOU2, Dan YANG3, Xin ZHAN4
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Abstract

We study the geometry and classification problems of biharmonic hypersurfaces in a pseudo-Euclidean 5-space Es5 (s=1,2,3,4). We prove that if Mr4 is a nondegenerate hypersurface in Es5 with diagonal shape operator, then Mr4 is minimal. Furthermore, based on the results due to Turgay et al. we show that any Lorentz biharmonic hypersurfaces in E15 is minimal. This result gives supporting answers to the biharmonic conjecture for hypersurfaces in 5-dimensional pseudo-Euclidean space.

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biharmonic maps / pseudo-Euclidean space / biharmonic hypersurfaces / biharmonic conjecture

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Yu FU, Zhong Hua HOU, Dan YANG, Xin ZHAN. Biharmonic Hypersurfaces in Es5. Acta Mathematica Sinica, Chinese Series, 2022, 65(2): 335-352 https://doi.org/10.12386/A2022sxxb0027

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