• Corpus ID: 221172823

# Biharmonic hypersurfaces in hemispheres

@article{Vieira2020BiharmonicHI,
title={Biharmonic hypersurfaces in hemispheres},
author={Matheus Vieira},
journal={arXiv: Differential Geometry},
year={2020}
}
• Matheus Vieira
• Published 19 August 2020
• Mathematics
• arXiv: Differential Geometry
In this paper, we consider the Balmus-Montaldo-Oniciuc's conjecture in the case of hemispheres. We prove that a compact non-minimal biharmonic hypersurface in a hemisphere of $S^{n+1}$ must be the small hypersphere $S^{n}\left(\frac{1}{\sqrt{2}}\right)$, provided that $n^{2}-H^{2}$ does not change sign.
Remarks on biharmonic hypersurfaces in space forms
We consider closed biharmonic hypersurfaces in the Euclidean sphere and prove a rigidity result under a suitable condition on the scalar curvature. Moreover, we establish an integral formula
Bi-eigenfunctions and biharmonic submanifolds in a sphere
In this note, we classify biharmonic submanifolds in a sphere defined by bieigenmaps (∆φ = λφ) or buckling eigenmaps (∆φ = −μ∆φ). The results can be viewed as generalizations of Takahashi’s
Biharmonic and biconservative hypersurfaces in space forms
• Mathematics
• 2020
We present some general properties of biharmonic and biconservative submanifolds and then survey recent results on such hypersurfaces in space forms. We also propose an alternative version for a

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