Intrinsic characterizations of biconservative surfaces in the 4-dimensional hyperbolic space
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913467856846848 |
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| author | Nistor, Simona Rusu, Mihaela |
| author_facet | Nistor, Simona Rusu, Mihaela |
| contents | In this paper, we extend the investigation of biconservative surfaces with parallel normalized mean curvature vector fields (PNMC) in the 4-dimensional space forms, focusing on the hyperbolic space \mathbb{H}^4, the last remaining case to explore. We establish that an abstract surface admits a PNMC biconservative immersion in \mathbb{H}^4 if and only if it satisfies a certain intrinsic condition; if such an immersion exists, it is unique. We further analyze these abstract surfaces, showing that they form a two-parameter family. Additionally, we provide three characterizations of the intrinsic condition to explore the geometric properties of these surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07359 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Intrinsic characterizations of biconservative surfaces in the 4-dimensional hyperbolic space Nistor, Simona Rusu, Mihaela Differential Geometry 53C42, 53B25 In this paper, we extend the investigation of biconservative surfaces with parallel normalized mean curvature vector fields (PNMC) in the 4-dimensional space forms, focusing on the hyperbolic space \mathbb{H}^4, the last remaining case to explore. We establish that an abstract surface admits a PNMC biconservative immersion in \mathbb{H}^4 if and only if it satisfies a certain intrinsic condition; if such an immersion exists, it is unique. We further analyze these abstract surfaces, showing that they form a two-parameter family. Additionally, we provide three characterizations of the intrinsic condition to explore the geometric properties of these surfaces. |
| title | Intrinsic characterizations of biconservative surfaces in the 4-dimensional hyperbolic space |
| topic | Differential Geometry 53C42, 53B25 |
| url | https://arxiv.org/abs/2408.07359 |