Geodesic
Local tube realizations of CR-manifolds and maximal Abelian subalgebras
Fels, Gregor1 ; kaup, Wilhelm1
1 Mathematisches Institut Universität Tübingen Auf der Morgenstelle 10 72076 Tübingen, Germany
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 1, pp. 99-128

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For every real-analytic CR-manifold M we give necessary and sufficient conditions that M can be realized in a suitable neighbourhood of a given point a∈M as a tube submanifold of some ℂ r . We clarify the question of the ‘right’ equivalence between two local tube realizations of the CR-manifold germ (M,a) by introducing two different notions of affine equivalence. One of our key results is a procedure that reduces the classification of equivalence classes to a purely algebraic manipulation in terms of Lie theory.

Publié le :
Classification : 32V05, 32V40, 32M25, 17B66

Fels, Gregor 1 ; kaup, Wilhelm 1

1 Mathematisches Institut Universität Tübingen Auf der Morgenstelle 10 72076 Tübingen, Germany 
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     title = {Local tube realizations of {CR-manifolds} and maximal {Abelian} subalgebras},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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     number = {1},
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Fels, Gregor; kaup, Wilhelm. Local tube realizations of CR-manifolds and maximal Abelian subalgebras. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 1, pp. 99-128. http://geodesic.mathdoc.fr/item/ASNSP_2011_5_10_1_99_0/