Canonical Cartan connections on maximally minimal generic submanifolds M^5 in C^4

Joël Merker (1) , Samuel Pocchiola (1) , Masoud Sabzevari (2)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 Department of Pure Mathematics [Shahrekord]

On a real analytic 5-dimensional CR-generic submanifold M^5 in C^4 of codimension 3 hence of CR dimension 1, which enjoys the generically satisfied nondegeneracy condition 5 = rank T^1,0 M + T^0,1M + [T^1,0M, T^0,1M] + [T^1,0M, [T^1,0M, T^0,1M]] + [T^1,0M, [T^1,0M, [T^1,0M, T^0,1M]]], a canonical Cartan connection is constructed after reduction to a certain partially explicit {e}-structure of the concerned local biholomorphic equivalence problem.

Mots clés: Nilpotent Lie algebra; Cartan equivalence problem; Cartan connection; Absorption of torsion; Normalization of group parameters; Prolongation of G-structures; Nilpotent Lie algebra

Domaines: Géométrie différentielle [math.DG]

Joël Merker, Samuel Pocchiola, Masoud Sabzevari. Canonical Cartan connections on maximally minimal generic submanifolds M^5 in C^4. Electronic Research Announcements in Mathematical Sciences, 2014, 21, pp.153 - 166. ⟨10.3934/era.2014.21.153⟩. ⟨hal-03286253⟩