λ-Biharmonic hypersurfaces in the product space L^m× ℝ

2024/03/16 by Chao Yang, Yang, Chao, Zhao Zhen +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2403.10816

openalex publication_date 2024/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study λ-biharmonic hypersurfaces in the product space L^m×ℝ, where L^m is an Einstein space and ℝ is a real line. We prove that λ-biharmonic hypersurfaces with constant mean curvature in L^m×ℝ are either minimal or vertical cylinders, and obtain some classification results for λ-biharmonic hypersurfaces under various constraints. Furthermore, we investigate λ-biharmonic hypersurfaces in the product space L^m(c)×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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