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2012 | 10 | 5 | 1801-1835
Tytuł artykułu

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

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EN
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.
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Bibliografia
  • [1] Aghasi M., Alizadeh B.M., Merker J., Sabzevari M., A Gröbner-bases algorithm for the computation of the cohomology of Lie (super) algebras, Adv. Appl. Clifford Algebr. (in press), DOI: 10.1007/s00006-011-0319-z
  • [2] Aghasi M., Merker J., Sabzevari M., Effective Cartan-Tanaka connections for C 6-smooth strongly pseudoconvex hypersurfaces M 3 ⊂ ℂ2, C. R. Math. Acad. Sci. Paris, 2011, 349(15–16), 845–848 http://dx.doi.org/10.1016/j.crma.2011.07.020
  • [3] Aghasi M., Merker J., Sabzevari M., Effective Cartan-Tanaka connections on C 6 strongly pseudoconvex hypersurfaces M 3 ⊂ ℂ2, preprint available at http://arxiv.org/abs/1104.1509
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Bibliografia
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bwmeta1.element.doi-10_2478_s11533-012-0052-4
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