On biharmonic hypersurfaces with constant scalar curvatures in 𝕊⁵

Fu, Yu

doi:10.1090/proc/12677

On biharmonic hypersurfaces with constant scalar curvatures in $\mathbb S^5$
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Proc. Amer. Math. Soc. 143 (2015), 5399-5409 Request permission

Abstract:

We prove that proper biharmonic hypersurfaces with constant scalar curvature in Euclidean sphere $\mathbb S^5$ must have constant mean curvature. Moreover, we also show that there exist no proper biharmonic hypersurfaces with constant scalar curvature in Euclidean space $\mathbb E^5$ or hyperbolic space $\mathbb H^5$, which give affirmative partial answers to Chen’s conjecture and the Generalized Chen’s conjecture.

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