New examples of CR submanifolds for the $2$-jet determination problem
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908423596015616 |
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| author | Bertrand, Florian Kolář, Martin Meylan, Francine |
| author_facet | Bertrand, Florian Kolář, Martin Meylan, Francine |
| contents | This paper addresses two questions related to mapping problems. In the first part of the paper, we discuss some recent results regarding the $2$-jet determination for biholomorphisms between smooth (weakly) pseudoconvex hypersurfaces; in light of those, we formulate a general problem and illustrate it with examples. In the second part of the paper, we provide a new example of a real submanifold of codimension $7$ in $\mathbb{C}^{10}$ that is not strictly pseudoconvex and for which its germs of CR automorphisms are determined by their $2$-jets at a given point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21221 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New examples of CR submanifolds for the $2$-jet determination problem Bertrand, Florian Kolář, Martin Meylan, Francine Complex Variables This paper addresses two questions related to mapping problems. In the first part of the paper, we discuss some recent results regarding the $2$-jet determination for biholomorphisms between smooth (weakly) pseudoconvex hypersurfaces; in light of those, we formulate a general problem and illustrate it with examples. In the second part of the paper, we provide a new example of a real submanifold of codimension $7$ in $\mathbb{C}^{10}$ that is not strictly pseudoconvex and for which its germs of CR automorphisms are determined by their $2$-jets at a given point. |
| title | New examples of CR submanifolds for the $2$-jet determination problem |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2506.21221 |