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”

A Frankel type theorem for CR submanifolds of Sasakian manifolds

Dario Di Pinto, Antonio Lotta (2023)

Archivum Mathematicum

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We prove a Frankel type theorem for $C R$ submanifolds of Sasakian manifolds, under suitable hypotheses on the index of the scalar Levi forms determined by normal directions. From this theorem we derive some topological information about $C R$ submanifolds of Sasakian space forms.

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 $Ω \cap V (z_{0})$ .

Totally contact umbilical screen-slant and screen-transversal lightlike submanifolds of indefinite Kenmotsu manifold

Payel Karmakar (2024)

Mathematica Bohemica

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We study totally contact umbilical screen-slant lightlike submanifolds and totally contact umbilical screen-transversal lightlike submanifolds of an indefinite Kenmotsu manifold. We prove a characterization theorem of totally contact umbilical screen-slant lightlike submanifolds of an indefinite Kenmotsu manifold. We further prove some results on a totally contact umbilical radical screen-transversal lightlike submanifold of an indefinite Kenmotsu manifold, such as the necessary and...

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]. ...

Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms

Shyamal K. Hui, Richard S. Lemence, Pradip Mandal (2020)

Commentationes Mathematicae Universitatis Carolinae

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A submanifold $M^{m}$ of a generalized Sasakian-space-form ${\bar{M}}^{2 n + 1} (f_{1}, f_{2}, f_{3})$ is said to be $C$ -totally real submanifold if $ξ \in Γ (T^{⊥} M)$ and $φ X \in Γ (T^{⊥} M)$ for all $X \in Γ (T M)$ . In particular, if $m = n$ , then $M^{n}$ is called Legendrian submanifold. Here, we derive Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms with respect to different connections; namely, quarter symmetric metric connection, Schouten-van Kampen connection and Tanaka-Webster connection.

On real flag manifolds with cup-length equal to its dimension

Marko Radovanović (2020)

Czechoslovak Mathematical Journal

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We prove that for any positive integers $n_{1}, n_{2}, ..., n_{k}$ there exists a real flag manifold $F (1, ..., 1, n_{1}, n_{2}, ..., n_{k})$ with cup-length equal to its dimension. Additionally, we give a necessary condition that an arbitrary real flag manifold needs to satisfy in order to have cup-length equal to its dimension.

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.