Fundamental Theorem for Submanifolds in General Ambient Spaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866929749076475904 |
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| author | Yu, Chengjie |
| author_facet | Yu, Chengjie |
| contents | In this paper, we extend the fundamental theorem for submanifolds to general ambient spaces by viewing it as a higher codimensional Cartan-Ambrose-Hicks theorem. The key ingredient in obtaining this is a generalization of development of curves in the positive codimensional case. One advantage of our results is that it also provide a geometric construction of the isometric immersion when the isometric immersion exists. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_03474 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Fundamental Theorem for Submanifolds in General Ambient Spaces Yu, Chengjie Differential Geometry In this paper, we extend the fundamental theorem for submanifolds to general ambient spaces by viewing it as a higher codimensional Cartan-Ambrose-Hicks theorem. The key ingredient in obtaining this is a generalization of development of curves in the positive codimensional case. One advantage of our results is that it also provide a geometric construction of the isometric immersion when the isometric immersion exists. |
| title | Fundamental Theorem for Submanifolds in General Ambient Spaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2109.03474 |