Minimal total absolute curvature for equiaffine immersions
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910091607801856 |
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| author | Yamauchi, Yuta |
| author_facet | Yamauchi, Yuta |
| contents | Koike (2001) defined the Lipschitz--Killing curvature and established a Chern--Lashof type inequality for equiaffine immersions of arbitrary codimensions. In this paper, we study the equality case. We prove that the total absolute curvature of an $n$-dimensional equiaffine immersion is equal to $2$ if and only if the image is a convex hypersurface embedded in an $(n+1)$-dimensional affine subspace. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00384 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Minimal total absolute curvature for equiaffine immersions Yamauchi, Yuta Differential Geometry Primary 53A15, Secondary 53C65, 53C42, 53C40 Koike (2001) defined the Lipschitz--Killing curvature and established a Chern--Lashof type inequality for equiaffine immersions of arbitrary codimensions. In this paper, we study the equality case. We prove that the total absolute curvature of an $n$-dimensional equiaffine immersion is equal to $2$ if and only if the image is a convex hypersurface embedded in an $(n+1)$-dimensional affine subspace. |
| title | Minimal total absolute curvature for equiaffine immersions |
| topic | Differential Geometry Primary 53A15, Secondary 53C65, 53C42, 53C40 |
| url | https://arxiv.org/abs/2604.00384 |