| Title:
|
Infinitesimal CR automorphisms of hypersurfaces of finite type in ${\mathbb{C}}^2$ (English) |
| Author:
|
Kolář, Martin |
| Author:
|
Meylan, Francine |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
47 |
| Issue:
|
5 |
| Year:
|
2011 |
| Pages:
|
367-375 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the Chern-Moser operator for hypersurfaces of finite type in ${\mathbb{C}}^2$. Analysing its kernel, we derive explicit results on jet determination for the stability group, and give a description of infinitesimal CR automorphisms of such manifolds. (English) |
| Keyword:
|
Chern-Moser operator |
| Keyword:
|
automorphism group |
| Keyword:
|
finite jet determination |
| Keyword:
|
finite type |
| MSC:
|
32V35 |
| MSC:
|
32V40 |
| idZBL:
|
Zbl 1265.32023 |
| idMR:
|
MR2876940 |
| . |
| Date available:
|
2011-12-16T15:24:55Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141784 |
| . |
| Reference:
|
[1] Baouendi, M. S., Ebenfelt, P., Rothschild, L. P.: Real Submanifolds in Complex Space and Their Mappings.Princeton Math. Ser. (1999). Zbl 0944.32040, MR 1668103 |
| Reference:
|
[2] Chern, S. S., Moser, J.: Real hypersurfaces in complex manifolds.Acta Math. 133 (1974), 219–271. MR 0425155, 10.1007/BF02392146 |
| Reference:
|
[3] Ebenfelt, P., Lamel, B., Zaitsev, D.: Finite jet determination of local analytic CR automorphisms and their parametrization by $2-$jets in the finite type case.Geom. Funct. Anal. 13 (2003), 546–573. Zbl 1032.32025, MR 1995799, 10.1007/s00039-003-0422-y |
| Reference:
|
[4] Kohn, J. J.: Boundary behaviour of $\bar{\partial }$ on weakly pseudoconvex manifolds of dimension two.J. Differential Geom. 6 (1972), 523–542. MR 0322365 |
| Reference:
|
[5] Kolář, M.: Normal forms for hypersurfaces of finite type in $ \mathbb{C}^2$.Math. Res. Lett. 12 (2005), 523–542. MR 2189248, 10.4310/MRL.2005.v12.n6.a10 |
| Reference:
|
[6] Kolář, M.: Local equivalence of symmetric hypersurfaces in $\mathbb{C}^2$.Trans. Amer. Math. Soc. 362 (2010), 2833–2843. MR 2592937, 10.1090/S0002-9947-10-05058-0 |
| Reference:
|
[7] Kolář, M., Meylan, F.: Chern–Moser operators and weighted jet determination problems.Contemporary Mathematics 550 (2011), 75–87. Zbl 1232.32024, MR 2868555, 10.1090/conm/550/10867 |
| . |
