For every real-analytic CR-manifold we give necessary and sufficient conditions that can be realized in a suitable neighbourhood of a given point as a tube submanifold of some . We clarify the question of the ‘right’ equivalence between two local tube realizations of the CR-manifold germ 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.
@article{ASNSP_2011_5_10_1_99_0, author = {Fels, Gregor and kaup, Wilhelm}, title = {Local tube realizations of {CR-manifolds} and maximal {Abelian} subalgebras}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {99--128}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 10}, number = {1}, year = {2011}, mrnumber = {2829317}, zbl = {1229.32020}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2011_5_10_1_99_0/} }
TY - JOUR AU - Fels, Gregor AU - kaup, Wilhelm TI - Local tube realizations of CR-manifolds and maximal Abelian subalgebras JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2011 SP - 99 EP - 128 VL - 10 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2011_5_10_1_99_0/ LA - en ID - ASNSP_2011_5_10_1_99_0 ER -
%0 Journal Article %A Fels, Gregor %A kaup, Wilhelm %T Local tube realizations of CR-manifolds and maximal Abelian subalgebras %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2011 %P 99-128 %V 10 %N 1 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2011_5_10_1_99_0/ %G en %F ASNSP_2011_5_10_1_99_0
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://www.numdam.org/item/ASNSP_2011_5_10_1_99_0/
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