Special normal form of a hyperbolic CR-manifold in ℂ⁴

Vladimir V. Ežov; Gerd Schmalz

Annales Polonici Mathematici (1998)

  • Volume: 70, Issue: 1, page 99-107
  • ISSN: 0066-2216

Abstract

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We give a special normal form for a non-semiquadratic hyperbolic CR-manifold M of codimension 2 in ℂ⁴, i.e., a construction of coordinates where the equation of M satisfies certain conditions. The coordinates are determined up to a linear coordinate change.

How to cite

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Vladimir V. Ežov, and Gerd Schmalz. "Special normal form of a hyperbolic CR-manifold in ℂ⁴." Annales Polonici Mathematici 70.1 (1998): 99-107. <http://eudml.org/doc/262678>.

@article{VladimirV1998,
abstract = {We give a special normal form for a non-semiquadratic hyperbolic CR-manifold M of codimension 2 in ℂ⁴, i.e., a construction of coordinates where the equation of M satisfies certain conditions. The coordinates are determined up to a linear coordinate change.},
author = {Vladimir V. Ežov, Gerd Schmalz},
journal = {Annales Polonici Mathematici},
keywords = {CR-manifolds; invariants; classification; hyperbolic CR manifold; semi-quadratic CR manifold; normal form},
language = {eng},
number = {1},
pages = {99-107},
title = {Special normal form of a hyperbolic CR-manifold in ℂ⁴},
url = {http://eudml.org/doc/262678},
volume = {70},
year = {1998},
}

TY - JOUR
AU - Vladimir V. Ežov
AU - Gerd Schmalz
TI - Special normal form of a hyperbolic CR-manifold in ℂ⁴
JO - Annales Polonici Mathematici
PY - 1998
VL - 70
IS - 1
SP - 99
EP - 107
AB - We give a special normal form for a non-semiquadratic hyperbolic CR-manifold M of codimension 2 in ℂ⁴, i.e., a construction of coordinates where the equation of M satisfies certain conditions. The coordinates are determined up to a linear coordinate change.
LA - eng
KW - CR-manifolds; invariants; classification; hyperbolic CR manifold; semi-quadratic CR manifold; normal form
UR - http://eudml.org/doc/262678
ER -

References

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  1. [CM74] S. S. Chern and J. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219-271. Zbl0302.32015
  2. [Lob88] A. V. Loboda, Generic real analytic manifolds of codimension 2 in ℂ⁴ and their biholomorphic mappings, Izv. Akad. Nauk SSSR Ser. Mat. 52 (1988), 970-990 (in Russian); English transl.: Math. USSR-Izv. 33 (1989), 295-315. Zbl0662.32018
  3. [Lob90] A. V. Loboda, Linearizability of holomorphic mappings of generating manifolds of codimension 2 in ℂ⁴, Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990), 632-644 (in Russian); English transl.: Math. USSR-Izv. 36 (1991), 655-667. Zbl0705.32011
  4. [Poi07] H. Poincaré, Les fonctions analytiques de deux variables et la représentation conforme, Rend. Circ. Mat. Palermo 23 (1907), 185-220. Zbl38.0459.02
  5. [Sch95] G. Schmalz, CR-Mannigfaltigkeiten höherer Kodimension und ihre Automorphismen, Habilitation thesis, Rheinische Friedrich-Wilhelms-Universität Bonn, 1995, to appear in Math. Nachr. 
  6. [Web78] S. M. Webster, On the Moser normal form at a non-umbilic point, Math. Ann. 233 (1978), 97-102. Zbl0358.32013

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