Kyoto Journal of Mathematics

Infinitesimal CR automorphisms and stability groups of infinite-type models in C2

Atsushi Hayashimoto and Ninh Van Thu

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Abstract

The purpose of this article is to give explicit descriptions for stability groups of real rigid hypersurfaces of infinite type in C2. The decompositions of infinitesimal CR automorphisms are also given.

Article information

Source
Kyoto J. Math., Volume 56, Number 2 (2016), 441-464.

Dates
Received: 20 October 2014
Revised: 30 March 2015
Accepted: 15 April 2015
First available in Project Euclid: 10 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1462901084

Digital Object Identifier
doi:10.1215/21562261-3478925

Mathematical Reviews number (MathSciNet)
MR3500847

Zentralblatt MATH identifier
1351.32060

Subjects
Primary: 32M05: Complex Lie groups, automorphism groups acting on complex spaces [See also 22E10]
Secondary: 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions 32H50: Iteration problems 32T25: Finite type domains

Keywords
holomorphic vector field automorphism group real hypersurface infinite-type point

Citation

Hayashimoto, Atsushi; Thu, Ninh Van. Infinitesimal CR automorphisms and stability groups of infinite-type models in $\mathbb{C}^{2}$. Kyoto J. Math. 56 (2016), no. 2, 441--464. doi:10.1215/21562261-3478925. https://projecteuclid.org/euclid.kjm/1462901084


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References

  • [A] M. Abate, “Discrete holomorphic local dynamical systems” in Holomorphic Dynamical Systems, Lecture Notes in Math. 1998, Springer, Berlin, 2010, 1–55.
  • [B] F. Bracci, Local dynamics of holomorphic diffeomorphisms, Boll. Unione Mat. Ital. 7 (2004), 609–636.
  • [CM] S. S. Chern and J. K. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219–271.
  • [D] J. P. D’Angelo, Real hypersurfaces, orders of contact, and applications, Ann. of Math. (2) 115 (1982), 615–637.
  • [EKS1] V. Ezhov, M. Kolář, and G. Schmalz, Degenerate hypersurfaces with a two-parametric family of automorphisms, Complex Var. Elliptic Equ. 54 (2009), 283–291.
  • [EKS2] V. Ezhov, M. Kolář, and G. Schmalz, Normal forms and symmetries of real hypersurfaces of finite type in $\mathbb{C}^{2}$, Indiana Univ. Math. J. 62 (2013), 1–32.
  • [KN] K.-T. Kim and N. V. Thu, On the tangential holomorphic vector fields vanishing at an infinite type point, Trans. Amer. Math. Soc. 367 (2015), 867–885.
  • [K1] M. Kolář, Normal forms for hypersurfaces of finite type in $\mathbb{C}^{2}$, Math. Res. Lett. 12 (2005), 897–910.
  • [K2] M. Kolář, Local symmetries of finite type hypersurfaces in $\mathbb{C}^{2}$, Sci. China Ser. A 49 (2006), 1633–1641.
  • [K3] M. Kolář, Local equivalence of symmetric hypersurfaces in $\mathbb{C}^{2}$, Trans. Amer. Math. Soc. 362, no. 6 (2010), 2833–2843.
  • [KM] M. Kolář and F. Meylan, Infinitesimal CR automorphisms of hypersurfaces of finite type in $\mathbb{C}^{2}$, Arch. Math. (Brno) 47 (2011), 367–375.
  • [KMZ] M. Kolář, F. Meylan, and D. Zaitsev, Chern-Moser operators and polynomial models in CR geometry, Adv. Math. 263 (2014), 321–356.
  • [N1] V. T. Ninh, On the existence of tangential holomorphic vector fields vanishing at an infinite type point, preprint, arXiv:1303.6156v7 [math.CV].
  • [N2] V. T. Ninh, On the CR automorphism group of a certain hypersurface of infinite type in $\mathbb{C}^{2}$, Complex Var. Elliptic Equ. 60 (2015), 977–991.
  • [NCM] V. T. Ninh, V. T. Chu, and A. D. Mai, On the real-analytic infinitesimal CR automorphism of hypersurfaces of infinite type, preprint, arXiv:1404.4914v2 [math.CV].
  • [S1] N. K. Stanton, Infinitesimal CR automorphisms of rigid hypersurfaces, Amer. J. Math. 117 (1995), 141–167.
  • [S2] N. K. Stanton, Infinitesimal CR automorphisms of real hypersurfaces, Amer. J. Math. 118 (1996), 209–233.