Canonical Cartan connections on maximally minimal generic submanifolds $\mathbf{M^5 \subset \mathbb{C}^4}$

Masoud Sabzevari; Joël Merker; Samuel Pocchiola

doi:10.3934/era.2014.21.153

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2014, Volume 21: 153-166. Doi: 10.3934/era.2014.21.153

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Canonical Cartan connections on maximally minimal generic submanifolds $\mathbf{M^5 \subset \mathbb{C}^4}$

1.
Department of Pure Mathematics, University of Shahrekord, 88186-34141 Shahrekord
2.
Département de Mathématiques d'Orsay, Bâtiment 425, Faculté des Sciences, F-91405 Orsay Cedex

Received: April 30, 2014

Revised: August 31, 2014

Published: January 2014

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Abstract

On a real analytic $5$-dimensional CR-generic submanifold $M^5 \subset \mathbb{C}^4$ of codimension $3$ hence of CR dimension $1$, which enjoys the generically satisfied nondegeneracy condition \begin{align*} {\bf 5} &= \text{rank}_\mathbb{C} \big( T^{1,0}M+T^{0,1}M + \big[T^{1,0}M,\,T^{0,1}M\big] \,+ \\&\qquad + \big[T^{1,0}M,\,[T^{1,0}M,T^{0,1}M]\big] + \big[T^{0,1}M,\,[T^{1,0}M,T^{0,1}M]\big] \big), \end{align*} a canonical Cartan connection is constructed after reduction to a certain partially explicit $\{ e\}$-structure of the concerned local biholomorphic equivalence problem.

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Mathematics Subject Classification: Primary 53B15, Secondary 32V40.

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References

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