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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.10816 |
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| _version_ | 1866916161343455232 |
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| author | Yang, Chao Zhao, Zhen |
| author_facet | Yang, Chao Zhao, Zhen |
| contents | In this paper, we study λ-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 λ-biharmonic hypersurfaces with constant mean curvature in L^{m}\times\mathbb{R} are either minimal or vertical cylinders, and obtain some classification results for λ$-biharmonic hypersurfaces under various constraints. Furthermore, we investigate λ-biharmonic hypersurfaces in the product space L^{m}(c)\times\mathbb{R}, where L^{m}(c) is a space form with constant sectional curvature c, and categorize hypersurfaces that are either totally umbilical or semi-parallel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10816 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | λ-Biharmonic hypersurfaces in the product space L^{m}\times \mathbb{R} Yang, Chao Zhao, Zhen Differential Geometry In this paper, we study λ-biharmonic hypersurfaces in the product space L^{m}\times\mathbb{R}, where L^{m} is an Einstein space and \mathbb{R} is a real line. We prove that λ-biharmonic hypersurfaces with constant mean curvature in L^{m}\times\mathbb{R} are either minimal or vertical cylinders, and obtain some classification results for λ$-biharmonic hypersurfaces under various constraints. Furthermore, we investigate λ-biharmonic hypersurfaces in the product space L^{m}(c)\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. |
| title | λ-Biharmonic hypersurfaces in the product space L^{m}\times \mathbb{R} |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2403.10816 |