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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2512.21217 |
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| _version_ | 1866918263290593280 |
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| author | Antas, Mateus |
| author_facet | Antas, Mateus |
| contents | In Moebius geometry there are two important tensors associated to an umbilic-free immersion $f:M^{n}\to \mathbb{S}^{m}$, namely the Moebius metric $\langle \cdot, \cdot \rangle^{*}$ and the Moebius second fundamental form $β$. In [11] was introduced the class of umbilic-free Moebius semi-parallel submanifolds of the unit sphere, which means that $\bar{R}\cdot β=0$, where $\bar{R}$ is the van der Waerden-Bortolotti curvature operator associated to $\langle \cdot, \cdot \rangle^{*}$. In this paper, we classify umbilic-free isometric immersions $f:M^{n}\to \mathbb{R}^{m}$ with semi-parallel Moebius second fundamental form and flat normal bundle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21217 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normally flat submanifolds with semi-parallel Moebius second fundamental form Antas, Mateus Differential Geometry In Moebius geometry there are two important tensors associated to an umbilic-free immersion $f:M^{n}\to \mathbb{S}^{m}$, namely the Moebius metric $\langle \cdot, \cdot \rangle^{*}$ and the Moebius second fundamental form $β$. In [11] was introduced the class of umbilic-free Moebius semi-parallel submanifolds of the unit sphere, which means that $\bar{R}\cdot β=0$, where $\bar{R}$ is the van der Waerden-Bortolotti curvature operator associated to $\langle \cdot, \cdot \rangle^{*}$. In this paper, we classify umbilic-free isometric immersions $f:M^{n}\to \mathbb{R}^{m}$ with semi-parallel Moebius second fundamental form and flat normal bundle. |
| title | Normally flat submanifolds with semi-parallel Moebius second fundamental form |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2512.21217 |