Hyperbolic-like manifolds, geometrical properties and holomorphic mappings

Grzegorz Boryczka; Luis Tovar

Displaying similar documents to “Hyperbolic-like manifolds, geometrical properties and holomorphic mappings”

Levi-flat filling of real two-spheres in symplectic manifolds (II)

Hervé Gaussier, Alexandre Sukhov (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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We consider a compact almost complex manifold $(M, J, ω)$ with smooth Levi convex boundary $\partial M$ and a symplectic tame form $ω$ . Suppose that $S^{2}$ is a real two-sphere, containing complex elliptic and hyperbolic points and generically embedded into $\partial M$ . We prove a result on filling $S^{2}$ by holomorphic discs.

A Kontinuitätssatz

Evgeni Chirka, Edgar Stout (1995)

Banach Center Publications

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A note on the Kobayashi pseudodistance and the tautness of holomorphic fiber bundles

Do Duc Thai, Nguyen Le Huong (1993)

Annales Polonici Mathematici

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We show a relation between the Kobayashi pseudodistance of a holomorphic fiber bundle and the Kobayashi pseudodistance of its base. Moreover, we prove that a holomorphic fiber bundle is taut iff both the fiber and the base are taut.

Remark on hyperbolic embeddability of relatively compact subspaces of complex spaces

Do Duc Thai (1991)

Annales Polonici Mathematici

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Abstract. The characterization of hyperbolic embeddability of relatively compact subspaces of a complex space in terms of extension of holomorphic maps from the punctured disc and of limit complex lines is given.

Hyperbolic Fourth-R Quadratic Equation and Holomorphic Fourth-R Polynomials

Apostolova, Lilia N. (2012)

Mathematica Balkanica New Series

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MSC 2010: 30C10, 32A30, 30G35 The algebra R(1; j; j2; j3), j4 = ¡1 of the fourth-R numbers, or in other words the algebra of the double-complex numbers C(1; j) and the corresponding functions, were studied in the papers of S. Dimiev and al. (see [1], [2], [3], [4]). The hyperbolic fourth-R numbers form other similar to C(1; j) algebra with zero divisors. In this note the square roots of hyperbolic fourth-R numbers and hyperbolic complex numbers are found. The quadratic equation...

The fixed points of holomorphic maps on a convex domain

Do Duc Thai (1992)

Annales Polonici Mathematici

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We give a simple proof of the result that if D is a (not necessarily bounded) hyperbolic convex domain in $ℂ^{n}$ then the set V of fixed points of a holomorphic map f:D → D is a connected complex submanifold of D; if V is not empty, V is a holomorphic retract of D. Moreover, we extend these results to the case of convex domains in a locally convex Hausdorff vector space.

An integral formula of hyperbolic type for solutions of the Dirac equation on Minkowski space with initial conditions on a hyperboloid

Martin Sikora (2010)

Archivum Mathematicum

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The Dirac equation for spinor-valued fields $f$ on the Minkowski space of even dimension form a hyperbolic system of partial differential equations. In the paper, we are showing how to reconstruct the solution from initial data given on the upper sheet $H^{+}$ of the hyperboloid. In particular, we derive an integral formula expressing the value of $f$ in a chosen point $p$ as an integral over a compact cycle given by the intersection of the null cone with $H^{+}$ in the Minkowski space $𝕄$ .

Injective hyperbolicity of domains

Marius Overholt (1995)

Annales Polonici Mathematici

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The pseudometric of Hahn is identical to the Kobayashi-Royden pseudometric on domains of dimension greater than two. Thus injective hyperbolicity coincides with ordinary hyperbolicity in this case.

Löbell manifolds revised.

Mednykh, A.D., Vesnin, A.Yu. (2007)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

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Elder siblings and the taming of hyperbolic 3-manifolds.

Freedman, Michael H., McMullen, Curtis T. (1998)

Annales Academiae Scientiarum Fennicae. Mathematica

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Some remarks on holomorphic extension in infinite dimensions

Pham Ban (1994)

Colloquium Mathematicae

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In finite-dimensional complex analysis, the extension of holomorphic maps has been investigated by many authors. In recent years some authors have considered this problem in the infinite-dimensional case. The aim of the present note is to study the extension of holomorphic maps with values in some Banach complex manifolds.