The infinitesimal deformations of hypersurfaces that preserve the Gauss map
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911755626610688 |
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| author | Dajczer, Marcos Jimenez, Miguel Ibieta |
| author_facet | Dajczer, Marcos Jimenez, Miguel Ibieta |
| contents | Classifying the nonflat hypersurfaces in Euclidean space $f\colon M^n\to\mathbb{R}^{n+1}$ that locally admit smooth infinitesimal deformations that preserve the Gauss map infinitesimally was a problem only considered by Schouten \cite{Sc} in 1928. He found two conditions that are necessary and sufficient, with the first one being the minimality of the submanifold. The second is a technical condition that does not clarify much about the geometric nature of the hypersurface. In that respect, the parametric solution of the problem given in this note yields that the submanifold has to be Kaehler. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_16086 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The infinitesimal deformations of hypersurfaces that preserve the Gauss map Dajczer, Marcos Jimenez, Miguel Ibieta Differential Geometry 53A07, 53B25 Classifying the nonflat hypersurfaces in Euclidean space $f\colon M^n\to\mathbb{R}^{n+1}$ that locally admit smooth infinitesimal deformations that preserve the Gauss map infinitesimally was a problem only considered by Schouten \cite{Sc} in 1928. He found two conditions that are necessary and sufficient, with the first one being the minimality of the submanifold. The second is a technical condition that does not clarify much about the geometric nature of the hypersurface. In that respect, the parametric solution of the problem given in this note yields that the submanifold has to be Kaehler. |
| title | The infinitesimal deformations of hypersurfaces that preserve the Gauss map |
| topic | Differential Geometry 53A07, 53B25 |
| url | https://arxiv.org/abs/2309.16086 |