\lambda-Biharmonic hypersurfaces in the product space L^{m}\times \mathbb{R}
Differential Geometry
2024-03-19 v1
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.
Cite
@article{arxiv.2403.10816,
title = {\lambda-Biharmonic hypersurfaces in the product space L^{m}\times \mathbb{R}},
author = {Chao Yang and Zhen Zhao},
journal= {arXiv preprint arXiv:2403.10816},
year = {2024}
}