Codimensions-Two Submanifolds Contained in the Light-like Hypercylinder $\mathcal{LC}^n\times\mathbb R$
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| Format: | Preprint |
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2025
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| _version_ | 1866912539581874176 |
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| author | Gineli, Ali Yürük, Hazal Turgay, Nurettin Cenk |
| author_facet | Gineli, Ali Yürük, Hazal Turgay, Nurettin Cenk |
| contents | In this paper, we investigate space-like codimension-two submanifolds of the Lorentz-Minkowski space $\mathbb{E}_1^{n+2}$ constrained to lie on the light-like hypercylinder $\mathcal{LC}^n \times \mathbb{R}$ over the light cone $\mathcal{LC}^n$. By constructing a geometrically defined global frame field on the submanifold, we analyze the geometric interpretations of the associated extrinsic invariants by providing characterizations of (pseudo-)isotropic and pseudo-umbilical submanifolds, as well as submanifolds with flat normal bundle. In particular, we obtain local classification theorems for these classes of submanifolds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_11653 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Codimensions-Two Submanifolds Contained in the Light-like Hypercylinder $\mathcal{LC}^n\times\mathbb R$ Gineli, Ali Yürük, Hazal Turgay, Nurettin Cenk Differential Geometry In this paper, we investigate space-like codimension-two submanifolds of the Lorentz-Minkowski space $\mathbb{E}_1^{n+2}$ constrained to lie on the light-like hypercylinder $\mathcal{LC}^n \times \mathbb{R}$ over the light cone $\mathcal{LC}^n$. By constructing a geometrically defined global frame field on the submanifold, we analyze the geometric interpretations of the associated extrinsic invariants by providing characterizations of (pseudo-)isotropic and pseudo-umbilical submanifolds, as well as submanifolds with flat normal bundle. In particular, we obtain local classification theorems for these classes of submanifolds. |
| title | Codimensions-Two Submanifolds Contained in the Light-like Hypercylinder $\mathcal{LC}^n\times\mathbb R$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2508.11653 |