The dimension function of holomorphic spaces of a real submanifold of an almost complex manifold

Fernando Etayo; Mario Fioravanti; Ujué R. Trías

Displaying similar documents to “The dimension function of holomorphic spaces of a real submanifold of an almost complex manifold”

Symmetric twofold CR submanifolds in a Euclidean space $R^{4 m}$

Minoru Kobayashi (1987)

Colloquium Mathematicae

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Almost invariant submanifolds for compact group actions

Alan Weinstein (2000)

Journal of the European Mathematical Society

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We define a $C^{1}$ distance between submanifolds of a riemannian manifold $M$ and show that, if a compact submanifold $N$ is not moved too much under the isometric action of a compact group $G$ , there is a $G$ -invariant submanifold $C^{1}$ -close to $N$ . The proof involves a procedure of averaging nearby submanifolds of riemannian manifolds in a symmetric way. The procedure combines averaging techniques of Cartan, Grove/Karcher, and de la Harpe/Karoubi with Whitney’s idea of realizing submanifolds as zeros...

Structure of a neighbourhood of a complex compact submanifold in a complex manifold

Roman Dwilewicz

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CONTENTSIntroduction...................................................................................................................................................................51. Notation and some definitions...................................................................................................................................6 (a) Analytic families.....................................................................................................................................................6 (b)...

On the normality of an almost contact $3$ -structure on $Q R$ -submanifolds

Shoichi Funabashi, Jin Suk Pak, Yang Jae Shin (2003)

Czechoslovak Mathematical Journal

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We study $n$ -dimensional $Q R$ -submanifolds of $Q R$ -dimension $(p - 1)$ immersed in a quaternionic space form $Q P^{(n + p) / 4} (c)$ , $c ≧ 0$ , and, in particular, determine such submanifolds with the induced normal almost contact $3$ -structure.

A result on extension of C.R. functions

Makhlouf Derridj, John Erik Fornaess (1983)

Annales de l'institut Fourier

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Let $Ω$ an open set in $C^{4}$ near $z_{0} \in \partial Ω$ , $λ$ a suitable holomorphic function near $z_{0}$ . If we know that we can solve the following problem (see [M. Derridj, Annali. Sci. Norm. Pisa, Série IV, vol. IX (1981)]) : $\overline{\partial} u = λ f$ , ( $f$ is a $(0, 1)$ form, $\overline{\partial}$ closed in $U (z_{0})$ in $U (z_{0})$ with supp $(u) \subset \overline{Ω} \cap U (z_{0})$ , then we deduce an extension result for $C . R .$ functions on $\partial Ω \cap U (z_{0})$ , as holomorphic fonctions in $Ω \cap V (z_{0})$ .

An extension theorem for separately holomorphic functions with analytic singularities

Marek Jarnicki, Peter Pflug (2003)

Annales Polonici Mathematici

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Let $D_{j} \subset ℂ^{k_{j}}$ be a pseudoconvex domain and let $A_{j} \subset D_{j}$ be a locally pluriregular set, j = 1,...,N. Put $X : = ⋃_{j = 1}^{N} A ₁ \times . . . \times A_{j - 1} \times D_{j} \times A_{j + 1} \times . . . \times A_{N} \subset ℂ^{k ₁ + . . . + k_{N}}$ . Let U be an open connected neighborhood of X and let M ⊊ U be an analytic subset. Then there exists an analytic subset M̂ of the “envelope of holomorphy” X̂ of X with M̂ ∩ X ⊂ M such that for every function f separately holomorphic on X∖M there exists an f̂ holomorphic on X̂∖M̂ with ${f ̂ |}_{X ∖ M} = f$ . The result generalizes special cases which were studied in [Ökt 1998], [Ökt 1999], [Sic 2001], and [Jar-Pfl 2001]. ...

Automorphism groups of minimal real-analytic CR manifolds

Robert Juhlin, Bernhard Lamel (2013)

Journal of the European Mathematical Society

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We show that the local automorphism group of a minimal real-analytic CR manifold $M$ is a finite dimensional Lie group if (and only if) $M$ is holomorphically nondegenerate by constructing a jet parametrization.

Levi's forms of higher codimensional submanifolds

Andrea D&#039;Agnolo, Giuseppe Zampieri (1991)

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

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Let $X ≅ C^{n}$ , let $M$ be a $C^{2}$ hypersurface of $X$ , $S$ be a $C^{2}$ submanifold of $M$ . Denote by $L_{M}$ the Levi form of $M$ at $z_{0} \in S$ . In a previous paper [3] two numbers $s^{\pm} (S, p)$ , $p \in {({\dot{T}}_{S}^{*} X)}_{z_{0}}$ are defined; for $S = M$ they are the numbers of positive and negative eigenvalues for $L_{M}$ . For $S \subset M$ , $p \in S \times_{M} \dot{T}^{*}_{S} X)$ , we show here that $s^{\pm} (S, p)$ are still the numbers of positive and negative eigenvalues for $L_{M}$ when restricted to $T_{z_{0}}^{C} S$ . Applications to the concentration in degree for microfunctions at the boundary are given.

Estimates of the Kobayashi-Royden metric in almost complex manifolds

Hervé Gaussier, Alexandre Sukhov (2005)

Bulletin de la Société Mathématique de France

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We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold $(M, J)$ admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the metric on a strictly pseudoconvex domain in $M$ and to give a sufficient condition for the complete hyperbolicity of a domain in $(M, J)$ .

Lagrangian fibrations on hyperkähler manifolds – On a question of Beauville

Daniel Greb, Christian Lehn, Sönke Rollenske (2013)

Annales scientifiques de l'École Normale Supérieure

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Let $X$ be a compact hyperkähler manifold containing a complex torus $L$ as a Lagrangian subvariety. Beauville posed the question whether $X$ admits a Lagrangian fibration with fibre $L$ . We show that this is indeed the case if $X$ is not projective. If $X$ is projective we find an almost holomorphic Lagrangian fibration with fibre $L$ under additional assumptions on the pair $(X, L)$ , which can be formulated in topological or deformation-theoretic terms. Moreover, we show that for any such almost holomorphic...