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...