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

DOI10.2478/s11533-012-0052-4zbMath1262.32040OpenAlexW2038383047WikidataQ126138757 ScholiaQ126138757MaRDI QIDQ1935625

Masoud Sabzevari, Joël Merker

Publication date: 18 February 2013

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s11533-012-0052-4

zbMATH Keywords

curvature functioncohomology of Lie algebrasBianchi identitiesdifferential algebrainfinitesimal CR automorphismsCartan connectionHeisenberg sphere

Mathematics Subject Classification ID

Real submanifolds in complex manifolds (32V40) Exterior differential systems (Cartan theory) (58A15) Cohomology of Lie (super)algebras (17B56) Derivations, actions of Lie algebras (16W25) Extension of functions and other analytic objects from CR manifolds (32V25)

Related Items (10)

Cartan equivalence problem for 5-dimensional bracket-generating CR manifolds in \(\mathbb C^4\) ⋮ Homogeneous CR and Para-CR structures in dimensions 5 and 3 ⋮ Totally nondegenerate models and standard manifolds in CR dimension one ⋮ Normal forms, moving frames, and differential invariants for nondegenerate hypersurfaces in \(\mathbb{C}^2\) ⋮ Moduli spaces of model real submanifolds: two alternative approaches ⋮ Parametric CR-umbilical locus of ellipsoids in \(\mathbb{C}^2\) ⋮ Applications of differential algebra for computing Lie algebras of infinitesimal CR-automorphisms ⋮ Rationality in Differential Algebraic Geometry ⋮ Biholomorphic equivalence to totally nondegenerate model CR manifolds ⋮ On the real-analyticity of rigid spherical hypersurfaces in ℂ²

Cites Work

• Cartan equivalence problem for 5-dimensional bracket-generating CR manifolds in \(\mathbb C^4\)
• Effective Cartan-Tanaka connections for \(\mathcal C^6\)-smooth strongly pseudoconvex hypersurfaces \(M^3 \subset \mathbb C^2\)
• A Gröbner-bases algorithm for the computation of the cohomology of Lie (super) algebras
• Cartan connections and Lie algebroids
• Cartan connections for CR manifolds
• Canonical Cartan connection and holomorphic invariants on Engel CR manifolds
• Real hypersurfaces in complex manifolds
• Holomorphic differential invariants for an ellipsoidal real hypersurface
• Parabolic geometries and canonical Cartan connections
• Nonalgebraizable real analytic tubes in \(\mathbb{C}^n\)
• Universal models for real submanifolds
• Lie symmetries and CR geometry
• Spherical tube hypersurfaces
• On differential systems, graded Lie algebras and pseudo-groups
• Nonrigid spherical real analytic hypersurfaces in ℂ²
• Holomorphic extension of CR functions, envelopes of holomorphy, and removable singularities
• Three-dimensional Cauchy–Riemann structures and second-order ordinary differential equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Explicit expression of Cartan's connection for Levi-nondegenerate 3-manifolds in complex surfaces, and identification of the Heisenberg sphere