Explicit expression of Cartan’s connection for Levi-nondegenerate 3-manifolds in complex surfaces, and identification of the Heisenberg sphere

Joël Merker; Masoud Sabzevari

Open Mathematics (2012)

  • Volume: 10, Issue: 5, page 1801-1835
  • ISSN: 2391-5455

Abstract

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We study effectively the Cartan geometry of Levi-nondegenerate C 6-smooth hypersurfaces M 3 in ℂ2. Notably, we present the so-called curvature function of a related Tanaka-type normal connection explicitly in terms of a graphing function for M, which is the initial, single available datum. Vanishing of this curvature function then characterizes explicitly the local biholomorphic equivalence of such M 3 ⊂ ℂ2 to the Heisenberg sphere ℍ3, such M’s being necessarily real analytic.

How to cite

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Joël Merker, and Masoud Sabzevari. "Explicit expression of Cartan’s connection for Levi-nondegenerate 3-manifolds in complex surfaces, and identification of the Heisenberg sphere." Open Mathematics 10.5 (2012): 1801-1835. <http://eudml.org/doc/269577>.

@article{JoëlMerker2012,
abstract = {We study effectively the Cartan geometry of Levi-nondegenerate C 6-smooth hypersurfaces M 3 in ℂ2. Notably, we present the so-called curvature function of a related Tanaka-type normal connection explicitly in terms of a graphing function for M, which is the initial, single available datum. Vanishing of this curvature function then characterizes explicitly the local biholomorphic equivalence of such M 3 ⊂ ℂ2 to the Heisenberg sphere ℍ3, such M’s being necessarily real analytic.},
author = {Joël Merker, Masoud Sabzevari},
journal = {Open Mathematics},
keywords = {Cartan connection; Heisenberg sphere; Cohomology of Lie algebras; Infinitesimal CR automorphisms; Differential algebra; Curvature function; Bianchi identities; cohomology of Lie algebras; infinitesimal CR automorphisms; differential algebra; curvature function},
language = {eng},
number = {5},
pages = {1801-1835},
title = {Explicit expression of Cartan’s connection for Levi-nondegenerate 3-manifolds in complex surfaces, and identification of the Heisenberg sphere},
url = {http://eudml.org/doc/269577},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Joël Merker
AU - Masoud Sabzevari
TI - Explicit expression of Cartan’s connection for Levi-nondegenerate 3-manifolds in complex surfaces, and identification of the Heisenberg sphere
JO - Open Mathematics
PY - 2012
VL - 10
IS - 5
SP - 1801
EP - 1835
AB - We study effectively the Cartan geometry of Levi-nondegenerate C 6-smooth hypersurfaces M 3 in ℂ2. Notably, we present the so-called curvature function of a related Tanaka-type normal connection explicitly in terms of a graphing function for M, which is the initial, single available datum. Vanishing of this curvature function then characterizes explicitly the local biholomorphic equivalence of such M 3 ⊂ ℂ2 to the Heisenberg sphere ℍ3, such M’s being necessarily real analytic.
LA - eng
KW - Cartan connection; Heisenberg sphere; Cohomology of Lie algebras; Infinitesimal CR automorphisms; Differential algebra; Curvature function; Bianchi identities; cohomology of Lie algebras; infinitesimal CR automorphisms; differential algebra; curvature function
UR - http://eudml.org/doc/269577
ER -

References

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