A characterization of the Legendre involution on the class of generic frontals
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914996883030016 |
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| author | Nishimura, Takashi |
| author_facet | Nishimura, Takashi |
| contents | We show that, under an additional mild assumption, on the class of generic frontals, any involution whose fixed point set is exactly the same as the fixed point set of the Legendre involution must be the Legendre involution (Theorem 2 in §1). Moreover, its natural complexification (Corollary 1 in §3) is simultaneously shown. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21957 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A characterization of the Legendre involution on the class of generic frontals Nishimura, Takashi Differential Geometry 57R45, 58C25 We show that, under an additional mild assumption, on the class of generic frontals, any involution whose fixed point set is exactly the same as the fixed point set of the Legendre involution must be the Legendre involution (Theorem 2 in §1). Moreover, its natural complexification (Corollary 1 in §3) is simultaneously shown. |
| title | A characterization of the Legendre involution on the class of generic frontals |
| topic | Differential Geometry 57R45, 58C25 |
| url | https://arxiv.org/abs/2410.21957 |