# Article

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Keywords:
Chern-Moser operator; automorphism group; finite jet determination; finite type
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.
References:
[1] Baouendi, M. S., Ebenfelt, P., Rothschild, L. P.: Real Submanifolds in Complex Space and Their Mappings. Princeton Math. Ser. (1999). MR 1668103 | Zbl 0944.32040
[2] Chern, S. S., Moser, J.: Real hypersurfaces in complex manifolds. Acta Math. 133 (1974), 219–271. DOI 10.1007/BF02392146 | MR 0425155
[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. DOI 10.1007/s00039-003-0422-y | MR 1995799 | Zbl 1032.32025
[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
[5] Kolář, M.: Normal forms for hypersurfaces of finite type in $\mathbb{C}^2$. Math. Res. Lett. 12 (2005), 523–542. DOI 10.4310/MRL.2005.v12.n6.a10 | MR 2189248
[6] Kolář, M.: Local equivalence of symmetric hypersurfaces in $\mathbb{C}^2$. Trans. Amer. Math. Soc. 362 (2010), 2833–2843. DOI 10.1090/S0002-9947-10-05058-0 | MR 2592937
[7] Kolář, M., Meylan, F.: Chern–Moser operators and weighted jet determination problems. Contemporary Mathematics 550 (2011), 75–87. DOI 10.1090/conm/550/10867 | MR 2868555 | Zbl 1232.32024

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