Browse > Article

CR MANIFOLDS OF ARBITRARY CODIMENSION WITH A CONTRACTION  

Kim, Sung-Yeon (DEPARTMENT OF MATHEMATICS EDUCATION, KANGWON NATIONAL UNIVERSITY)
Publication Information
The Pure and Applied Mathematics / v.17, no.2, 2010 , pp. 157-165 More about this Journal
Abstract
Let (M,p) be a germ of a $C^{\infty}$ CR manifold of CR dimension n and CR codimension d. Suppose (M,p) admits a $C^{\infty}$ contraction at p. In this paper, we show that (M,p) is CR equivalent to a generic submanifold in $\mathbb{C}^{n+d}$ defined by a vector valued weighted homogeneous polynomial.
Keywords
CR manifold; CR map; contraction;
Citations & Related Records
연도 인용수 순위
  • Reference
1 K.T. Kim & S.Y. Kim: CR hypersurfaces with a contracting automorphism. J. Geom. Anal. 18 (2008), no. 3, 800-834.   DOI   ScienceOn
2 B. Wong: Characterization of the unit ball in $C^n$ by its automorphism group. Invent. Math. 41 (1977), no. 3, 253-257.   DOI
3 J.P. Rosay: Sur une caracterisation de la boule parmi les domaines de $C^n$ par son groupe d'automorphismes. Ann. Inst. Fourier (Grenoble) 29 (1979), no. 4, ix, 91-97.   DOI
4 J.P. D'Angelo: Real hypersurfaces, orders of contact, and applications. Ann. of Math. (2) 115 (1982), no. 3, 615-637.   DOI   ScienceOn
5 N. Tanaka: On the pseudoconformal geometry of hypersurfaces of the space of n complex variables. J. Math. Soc. Japan 14 (1962), 397-429.   DOI
6 T. Ueda: Normal forms of attracting holomorphic maps. Math. J. of Toyama Univ. 22 (1999), 25-34.
7 M.S. Baouendi, P. Ebenfelt, & L.P. Rothschild: Real Submanifolds in Complex Space and Their mappings. Princeton Math. Series 47, Princeton Univ. Press, New Jersey, 1999.
8 M.S. Baouendi, L.P. Rothschild & F. Treves: CR structures with group action and extendability of CR functions. Invent. Math. 82 (1985), no. 2, 359-396.   DOI
9 F. Berteloot: Methodes de changement d'echelles en analyse complexe. A draft for lectures at C.I.R.M. (Luminy, France) in 2003.
10 D.W. Catlin: Boundary invariants of pseudoconvex domains. Ann. of Math. (2) 120 (1984), no. 3, 529-586.   DOI   ScienceOn
11 K.T. Kim & J.C. Yoccoz: CR manifolds admitting a CR contraction. preprint. (arXiv:0807.0482)
12 S. Kobayashi: Hyperbolic complex spaces. Grundlehren der Mathematischen Wis- senschaften [Fundamental Principles of Mathematical Sciences], 318. Springer-Verlag, Berlin, 1998.
13 S.G. Krantz: Function theory of several complex variables. AMS Chelsea, Amer. Math. Soc. 1992.