Local tube realizations of CR-manifolds and maximal Abelian subalgebras
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 1, p. 99-128

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 $a\in M$ 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 $\left(M,a\right)$ 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.

Published online : 2018-06-21
Classification:  32V05,  32V40,  32M25,  17B66
@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},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 10},
number = {1},
year = {2011},
pages = {99-128},
zbl = {1229.32020},
mrnumber = {2829317},
language = {en},
url = {http://www.numdam.org/item/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, Serie 5, Volume 10 (2011) no. 1, pp. 99-128. http://www.numdam.org/item/ASNSP_2011_5_10_1_99_0/

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