Displaying similar documents to “Remarks on CR-manifolds of codimension 2 in C 4 ”

Generic subgroups of Aut 𝔹 n

Chiara de Fabritiis (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We prove that for a parabolic subgroup Γ of Aut 𝔹 n the fixed points sets of all elements in Γ ∖ { id 𝔹 n } are the same. This result, together with a deep study of the structure of subgroups of Aut 𝔹 n acting freely and properly discontinuously on 𝔹 n , entails a generalization of the so called weak Hurwitz’s theorem: namely that, given a complex manifold X covered by 𝔹 n and such that the group of deck transformations of the covering is “sufficiently generic”, then id X is isolated in Hol ( X , X ) .

Unique determination of local C ⁢ R -maps by their jets: a survey

Dmitri Zaitsev (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We survey results on unique determination of local C ⁢ R -automorphisms of smooth C ⁢ R -manifolds and of local biholomorphisms of real-analytic C ⁢ R -submanifolds of complex spaces by their jets of finite order at a given point. Examples generalizing [28] are given showing that the required jet order may be arbitrarily high.

Special normal form of a hyperbolic CR-manifold in ℂ⁴

Vladimir V. Ežov, Gerd Schmalz (1998)

Annales Polonici Mathematici

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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.

Some special geometry in dimension six

Čap, Andreas, Eastwood, Michael

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Motivated by the study of CR-submanifolds of codimension  2 in  ℂ 4 , the authors consider here a 6 -dimensional oriented manifold  M equipped with a 4 -dimensional distribution. Under some non-degeneracy condition, two different geometric situations can occur. In the elliptic case, one constructs a canonical almost complex structure on  M ; the hyperbolic case leads to a canonical almost product structure. In both cases the only local invariants are given by the obstructions to integrability...

Decomposition of CR-manifolds and splitting of CR-maps

Atsushi Hayashimoto, Sung-Yeon Kim, Dmitri Zaitsev (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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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...

Free CR distributions

Gerd Schmalz, Jan Slovák (2012)

Open Mathematics

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There are only some exceptional CR dimensions and codimensions such that the geometries enjoy a discrete classification of the pointwise types of the homogeneous models. The cases of CR dimensions n and codimensions n 2 are among the very few possibilities of the so-called parabolic geometries. Indeed, the homogeneous model turns out to be PSU(n+1,n)/P with a suitable parabolic subgroup P. We study the geometric properties of such real (2n+n 2)-dimensional submanifolds in ℂ n + n 2 for all n...