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

• DOI: 10.48550/arxiv.2403.10816
• Publication Date: 2024-03-16
• Authors: Chao Yang; Zhao Zhen
• Keywords: Biharmonic equation

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