On the local geometry of generic submanifolds of \(\mathbb C^n\) and the analytic reflection principle. I.

DOI10.1007/s10958-005-0063-9zbMath1084.32026arXivmath/0404249OpenAlexW2333778570MaRDI QIDQ2487431

Joël Merker

Publication date: 5 August 2005

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0404249

zbMATH Keywords

reflection principlegeneric CR manifold

Mathematics Subject Classification ID

Real submanifolds in complex manifolds (32V40) Extension of functions and other analytic objects from CR manifolds (32V25)

Related Items (8)

Cartan equivalence problem for 5-dimensional bracket-generating CR manifolds in \(\mathbb C^4\) ⋮ Vanishing Hachtroudi curvature and local equivalence to the Heisenberg pseudosphere ⋮ Lie-Cartan differential invariants and Poincaré-Moser normal forms: Conflunces ⋮ Some aspects of holomorphic mappings: a survey ⋮ Effective Cartan-Tanaka connections for \(\mathcal C^6\)-smooth strongly pseudoconvex hypersurfaces \(M^3 \subset \mathbb C^2\) ⋮ Analytic sets extending the graphs of holomorphic mappings between domains of different dimensions ⋮ Lie symmetries and CR geometry ⋮ Propagation of analyticity for essentially finite \(\mathcal C^\infty\)-smooth CR mappings

Cites Work

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• Analyticity of CR equivalences between some real hypersurfaces in \(C^ n\) with degenerate Levi forms
• Proper holomorphic mappings between real-analytic pseudoconvex domains in \({\mathbb{C}}^ n\)
• A reflection principle for degenerate real hypersurfaces
• Real hypersurfaces in complex manifolds
• On CR mappings of real quadric manifolds
• Sur la géométrie pseudo-conforme des hypersurfaces de l'espace de deux variables complexes
• The Bergman kernel and biholomorphic mappings of pseudoconvex domains
• Infinitesimal CR Automorphisms of Real Hypersurfaces
• On 𝐶𝑅-mappings between algebraic Cauchy-Riemann manifolds and separate algebraicity for holomorphic functions
• Segre varieties and Lie symmetries

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