Surfaces with flat normal connection in 4-dimensional space forms
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866918356910604288 |
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| author | Ando, Naoya Hatanaka, Ryusei |
| author_facet | Ando, Naoya Hatanaka, Ryusei |
| contents | Let $N$ be a Riemannian, Lorentzian or neutral $4$-dimensional space form with constant sectional curvature $L_0$. In this paper, noticing the linearly dependent condition, we obtain characterizations of space-like surfaces in $N$ with flat normal connection and parallel normal vector fields. In addition, we obtain a generic characterization of space-like surfaces in $N$ with flat normal connection and $K\equiv L_0$ which do not admit any parallel normal vector fields. For time-like surfaces in $N$ with flat normal connection, we obtain analogous results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15780 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Surfaces with flat normal connection in 4-dimensional space forms Ando, Naoya Hatanaka, Ryusei Differential Geometry Let $N$ be a Riemannian, Lorentzian or neutral $4$-dimensional space form with constant sectional curvature $L_0$. In this paper, noticing the linearly dependent condition, we obtain characterizations of space-like surfaces in $N$ with flat normal connection and parallel normal vector fields. In addition, we obtain a generic characterization of space-like surfaces in $N$ with flat normal connection and $K\equiv L_0$ which do not admit any parallel normal vector fields. For time-like surfaces in $N$ with flat normal connection, we obtain analogous results. |
| title | Surfaces with flat normal connection in 4-dimensional space forms |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2501.15780 |