\lambda-Biharmonic hypersurfaces in the product space L^{m}\times \mathbb{R}

Chao Yang; Zhen Zhao

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arXiv · 2403.10816

\lambda-Biharmonic hypersurfaces in the product space L^{m}\times \mathbb{R}

Chao Yang·Zhen Zhao

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Abstract

In this paper, we study \lambda-biharmonic hypersurfaces in the product space L^{m}\times\mathbb{R}, where L^{m} is an Einstein space and \mathbb{R} is a real line. We prove that \lambda-biharmonic hypersurfaces with constant mean curvature in L^{m}\times\mathbb{R} are either minimal or vertical cylinders, and obtain some classification results for \lambda$-biharmonic hypersurfaces under various constraints. Furthermore, we investigate \lambda-biharmonic hypersurfaces in the product space L^{m}(c)\times\mathbb{R}, where L^{m}(c) is a space form with constant sectional curvature c, and categorize hypersurfaces that are either totally umbilical or semi-parallel.

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BibTeX RIS

Chao Yang, Zhen Zhao. 2024-03-16. \lambda-Biharmonic hypersurfaces in the product space L^{m}\times \mathbb{R}. https://arxiv.org/abs/2403.10816

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