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Canvexité rationnelle des surfaces lagrangiennes.

Julien Duval (1991)

Inventiones mathematicae

Cartan-Chern-Moser theory on algebraic hypersurfaces and an application to the study of automorphism groups of algebraic domains

Xiaojun Huang, Shanyu Ji (2002)

Annales de l’institut Fourier

For a strongly pseudoconvex domain $D \subset ℂ^{n + 1}$ defined by a real polynomial of degree $k_{0}$ , we prove that the Lie group $Aut (D)$ can be identified with a constructible Nash algebraic smooth variety in the CR structure bundle $Y$ of $\partial D$ , and that the sum of its Betti numbers is bounded by a certain constant $C_{n, k_{0}}$ depending only on $n$ and $k_{0}$ . In case $D$ is simply connected, we further give an explicit but quite rough bound in terms of the dimension and the degree of the defining polynomial. Our approach is to adapt the Cartan-Chern-Moser...

Cauchy-Kowalewski extension theorems and representations of analytic functionals acting over special classes of real n-dimensional submanifolds of $C^{(} n + 1)$

Ryan, John (1984)

Proceedings of the 11th Winter School on Abstract Analysis

Chaînes holomorphes de bord donné dans $ℂ P^{n}$

Pierre Dolbeault, Gennadi Henkin (1997)

Bulletin de la Société Mathématique de France

Classification of CR invariant structures for compact Lie groups. (Classification des structures CR invariantes pour les groupes de Lie compacts.)

Charbonnel, Jean-Yves, Ounaïes-Khalgui, Hella (2004)

Journal of Lie Theory

Complex-Tangential Sets and Boundary Values in Submanifolds of the Boundary.

A. Noell, W.C. Ramey, D.C. Ullrich (1987)

Mathematische Zeitschrift

Convergence of formal invertible CR mappings between minimal holomorphically nondegenerate real analytic hypersurfaces.

Merker, Joël (2001)

International Journal of Mathematics and Mathematical Sciences

CR mappings between real hypersurfaces in complex space

M. S. Baouendi, L. P. Rothschild (1987/1988)

Séminaire Équations aux dérivées partielles (Polytechnique)

CR singular immersions of complex projective spaces.

Coffman, Adam (2002)

Beiträge zur Algebra und Geometrie

CR structures with group action and extendability of CR function.

M.S. Baouendi, L.P. Rothschild (1985)

Inventiones mathematicae

CR submanifolds of maximal CR dimension in complex manifolds

Mirjana Djorić, Masafumi Okumura (2002)

Banach Center Publications

The aim of this paper is to investigate n-dimensional real submanifolds of complex manifolds in the case when the maximal holomorphic tangent space is (n-1)-dimensional. In particular, we give some examples and we consider the Levi form on these submanifolds, especially when the ambient space is a complex space form. Moreover, we show that on some remarkable class of real hypersurfaces of complex space forms, the Levi form cannot vanish identically.

Cylindrical real hyper surfaces in $\mathbf{C}^{n}$

Claudio Rea (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si stabiliscono due condizioni sufficienti per un germe di ipersuperficie reale di classe $c^{\infty}$ in $\mathbf{C}^{n}$ affinchè esistano coordinate olomorfe rispetto alle quali l'ipersuperficie risulti essere il luogo di zeri di una funzione di $k<n$ variabili e $k$ sia minimale rispetto a questa proprietà. In altre parole si vuole che l'ipersuperficie, a meno di una trasformazione bi-olomorfa, sia l’unione di sottovarietà lineari complesse, parallele di dimensione $n — k$ .

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