Displaying similar documents to “Three-dimensional complex homogeneous complex contact manifolds.”

Normal forms of invariant vector fields under a finite group action.

Federico Sánchez-Bringas (1993)

Publicacions Matemàtiques

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Let Γ be a finite subgroup of GL(n, C). This subgroup acts on the space of germs of holomorphic vector fields vanishing at the origin in C and on the group of germs of holomorphic diffeomorphisms of (C, 0). We prove a theorem of invariant conjugacy to a normal form and linearization for the subspace of invariant germs of holomorphic vector fields and we give a description of this type of normal forms in dimension n = 2.

Oka manifolds: From Oka to Stein and back

Franc Forstnerič (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

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Oka theory has its roots in the classical Oka-Grauert principle whose main result is Grauert’s classification of principal holomorphic fiber bundles over Stein spaces. Modern Oka theory concerns holomorphic maps from Stein manifolds and Stein spaces to Oka manifolds. It has emerged as a subfield of complex geometry in its own right since the appearance of a seminal paper of M. Gromov in 1989. In this expository paper we discuss Oka manifolds and Oka maps. We describe equivalent...

Symmetries of holomorphic geometric structures on tori

Sorin Dumitrescu, Benjamin McKay (2016)

Complex Manifolds

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We prove that any holomorphic locally homogeneous geometric structure on a complex torus of dimension two, modelled on a complex homogeneous surface, is translation invariant. We conjecture that this result is true in any dimension. In higher dimension, we prove it for G nilpotent. We also prove that for any given complex algebraic homogeneous space (X, G), the translation invariant (X, G)-structures on tori form a union of connected components in the deformation space of (X, G)-structures. ...