Decomposition of CR-manifolds and splitting of CR-maps

Atsushi Hayashimoto; Sung-Yeon Kim; Dmitri Zaitsev

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2003)

  • Volume: 2, Issue: 3, page 433-448
  • ISSN: 0391-173X

Abstract

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We show the uniqueness of local and global decompositions of abstract CR-manifolds into direct products of irreducible factors, and a splitting property for their CR-diffeomorphisms into direct products with respect to these decompositions. The assumptions on the manifolds are finite non-degeneracy and finite-type on a dense subset. In the real-analytic case, these are the standard assumptions that appear in many other questions. In the smooth case, the assumptions cannot be weakened by replacing “dense” with “open” as is demonstrated by an example. An application to the cancellation problem is also given. The proof is based on the development of methods of [BER99b], [BRZ00], [KZ01] and the use of “approximate infinitesimal automorphisms” introduced in this paper.

How to cite

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Hayashimoto, Atsushi, Kim, Sung-Yeon, and Zaitsev, Dmitri. "Decomposition of CR-manifolds and splitting of CR-maps." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 2.3 (2003): 433-448. <http://eudml.org/doc/84507>.

@article{Hayashimoto2003,
abstract = {We show the uniqueness of local and global decompositions of abstract CR-manifolds into direct products of irreducible factors, and a splitting property for their CR-diffeomorphisms into direct products with respect to these decompositions. The assumptions on the manifolds are finite non-degeneracy and finite-type on a dense subset. In the real-analytic case, these are the standard assumptions that appear in many other questions. In the smooth case, the assumptions cannot be weakened by replacing “dense” with “open” as is demonstrated by an example. An application to the cancellation problem is also given. The proof is based on the development of methods of [BER99b], [BRZ00], [KZ01] and the use of “approximate infinitesimal automorphisms” introduced in this paper.},
author = {Hayashimoto, Atsushi, Kim, Sung-Yeon, Zaitsev, Dmitri},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {3},
pages = {433-448},
publisher = {Scuola normale superiore},
title = {Decomposition of CR-manifolds and splitting of CR-maps},
url = {http://eudml.org/doc/84507},
volume = {2},
year = {2003},
}

TY - JOUR
AU - Hayashimoto, Atsushi
AU - Kim, Sung-Yeon
AU - Zaitsev, Dmitri
TI - Decomposition of CR-manifolds and splitting of CR-maps
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2003
PB - Scuola normale superiore
VL - 2
IS - 3
SP - 433
EP - 448
AB - We show the uniqueness of local and global decompositions of abstract CR-manifolds into direct products of irreducible factors, and a splitting property for their CR-diffeomorphisms into direct products with respect to these decompositions. The assumptions on the manifolds are finite non-degeneracy and finite-type on a dense subset. In the real-analytic case, these are the standard assumptions that appear in many other questions. In the smooth case, the assumptions cannot be weakened by replacing “dense” with “open” as is demonstrated by an example. An application to the cancellation problem is also given. The proof is based on the development of methods of [BER99b], [BRZ00], [KZ01] and the use of “approximate infinitesimal automorphisms” introduced in this paper.
LA - eng
UR - http://eudml.org/doc/84507
ER -

References

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