no. 15-16
Complex Analysis/Mathematical Analysis
Effective Cartan–Tanaka connections for C6-smooth strongly pseudoconvex hypersurfaces M3⊂C2
[Connections de Cartan–Tanaka effectives pour les hypersurfaces strictement pseudoconvexes M3⊂C2 de classe C6]

Présenté par : Jean-Pierre Demailly

Aghasi, Mansour1 ; Merker, Joël2 ; Sabzevari, Masoud1
1 Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran
2 Département de mathématiques dʼOrsay, bâtiment 425, faculté des sciences, 91405 Orsay cedex, France
Comptes Rendus. Mathématique, Tome 349 (2011) no. 15-16, pp. 845-848.

Des courbures de Cartan–Tanaka explicites, dont lʼannulation identique caractérise la sphéricité, sont fournies en termes du jet dʼordre 6 dʼune fonction graphante pour une hypersurface M3⊂C2 de classe C6 strictement pseudoconvexe.

Explicit Cartan–Tanaka curvatures, the vanishing of which characterizes sphericity, are provided in terms of the 6-th order jet of a graphing function for a C6 strongly pseudoconvex hypersurface M3⊂C2.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.07.020
Aghasi, Mansour 1 ; Merker, Joël 2 ; Sabzevari, Masoud 1

1 Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran
2 Département de mathématiques dʼOrsay, bâtiment 425, faculté des sciences, 91405 Orsay cedex, France 
@article{CRMATH_2011__349_15-16_845_0,
     author = {Aghasi, Mansour and Merker, Jo\"el and Sabzevari, Masoud},
     title = {Effective {Cartan{\textendash}Tanaka} connections for $ {\mathcal{C}}^{6}$-smooth strongly pseudoconvex hypersurfaces $ {M}^{3}\subset {\mathbb{C}}^{2}$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {845--848},
     publisher = {Elsevier},
     volume = {349},
     number = {15-16},
     year = {2011},
     doi = {10.1016/j.crma.2011.07.020},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2011.07.020/}
}
TY  - JOUR
AU  - Aghasi, Mansour
AU  - Merker, Joël
AU  - Sabzevari, Masoud
TI  - Effective Cartan–Tanaka connections for $ {\mathcal{C}}^{6}$-smooth strongly pseudoconvex hypersurfaces $ {M}^{3}\subset {\mathbb{C}}^{2}$
JO  - Comptes Rendus. Mathématique
PY  - 2011
SP  - 845
EP  - 848
VL  - 349
IS  - 15-16
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2011.07.020/
DO  - 10.1016/j.crma.2011.07.020
LA  - en
ID  - CRMATH_2011__349_15-16_845_0
ER  - 
%0 Journal Article
%A Aghasi, Mansour
%A Merker, Joël
%A Sabzevari, Masoud
%T Effective Cartan–Tanaka connections for $ {\mathcal{C}}^{6}$-smooth strongly pseudoconvex hypersurfaces $ {M}^{3}\subset {\mathbb{C}}^{2}$
%J Comptes Rendus. Mathématique
%D 2011
%P 845-848
%V 349
%N 15-16
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2011.07.020/
%R 10.1016/j.crma.2011.07.020
%G en
%F CRMATH_2011__349_15-16_845_0
Aghasi, Mansour; Merker, Joël; Sabzevari, Masoud. Effective Cartan–Tanaka connections for $ {\mathcal{C}}^{6}$-smooth strongly pseudoconvex hypersurfaces $ {M}^{3}\subset {\mathbb{C}}^{2}$. Comptes Rendus. Mathématique, Tome 349 (2011) no. 15-16, pp. 845-848. doi : 10.1016/j.crma.2011.07.020. http://www.numdam.org/articles/10.1016/j.crma.2011.07.020/

[1] M. Aghasi, B. Alizadeh, J. Merker, M. Sabzevari, A Gröbner-bases algorithm for the computation of the cohomology of Lie (super) algebras, , 23 pp. | arXiv

[2] M. Aghasi, J. Merker, M. Sabzevari, Effective Cartan–Tanaka connections on C6 strongly pseudoconvex hypersurfaces M3⊂C2, http://ariv.org/abs/1104.1509, 113 pp.

[3] Beloshapka, V.K.; Ezhov, V.; Schmalz, G. Canonical Cartan connection and holomorphic invariants on Engel CR manifolds, J. Math. Phys., Volume 14 (2007), pp. 121-133 (in Russian)

[4] Čap, A.; Schichl, H. Parabolic geometries and canonical Cartan connections, Hokkaido Math. J., Volume 29 (2000), pp. 453-505

[5] Cartan, É.; Cartan, É. Sur la géométrie pseudo-conforme des hypersurfaces de deux variables complexes II, Ann. Sc. Norm. Super. Pisa, Volume 4 (1932), pp. 17-90

[6] Ezhov, V.; McLaughlin, B.; Schmalz, G. From Cartan to Tanaka: getting real in the complex world, Notices of the AMS, Volume 58 (2011), pp. 20-27

[7] Merker, J. On the partial algebraicity of holomorphic mappings between two real algebraic sets, Bull. Soc. Math. France, Volume 129 (2001), pp. 547-591

[8] Merker, J. On the local geometry of generic submanifolds of Cn and the analytic reflection principle, J. Math. Sci. (N. Y.), Volume 125 (2005), pp. 751-824

[9] Merker, J. Lie symmetries and CR geometry, J. Math. Sci. (N. Y.), Volume 154 (2008), pp. 817-922

[10] Merker, J. Nonrigid spherical real analytic hypersurfaces in C2, Complex Var. Elliptic Equ., Volume 55 (2010) no. 12, pp. 1155-1182

[11] Merker, J.; Porten, E. Holomorphic extension of CR functions, envelopes of holomorphy and removable singularities, Int. Math. Res. Surv. (2006) (Article ID 28295, 287 pp)

[12] Sharpe, R.W. Differential Geometry, Cartanʼs Generalization of Kleinʼs Erlangen Program, Springer, Berlin, 1997

[13] Tanaka, N. On differential systems, graded Lie algebras and pseudo-groups, J. Math. Kyoto Univ., Volume 10 (1970), pp. 1-82

Cité par Sources :