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On holomorphically separable complex solv-manifolds

Alan T. Huckleberry, E. Oeljeklaus (1986)

Annales de l'institut Fourier

Let G be a solvable complex Lie group and H a closed complex subgroup of G . If the global holomorphic functions of the complex manifold X : G / H locally separate points on X , then X is a Stein manifold. Moreover there is a subgroup H ^ of finite index in H with π 1 ( G / H ^ ) nilpotent. In special situations (e.g. if H is discrete) H normalizes H ^ and H / H ^ is abelian.

On homological index

Bahman Khanedani (2000)

Annales de la Faculté des sciences de Toulouse : Mathématiques

On invariant domains in certain complex homogeneous spaces

Xiang-Yu Zhou (1997)

Annales de l'institut Fourier

Given a compact connected Lie group K . For a relatively compact K -invariant domain D in a Stein K ℂ -homogeneous space, we prove that the automorphism group of D is compact and if K is semisimple, a proper holomorphic self mapping of D is biholomorphic.

On irreducible components of a Weierstrass-type variety

Romuald A. Janik (1997)

Annales Polonici Mathematici

We give a characterization of the irreducible components of a Weierstrass-type (W-type) analytic (resp. algebraic, Nash) variety in terms of the orbits of a Galois group associated in a natural way to this variety. Since every irreducible variety of pure dimension is (locally) a component of a W-type variety, this description may be applied to any such variety.

On isometries of the carathéodory and Kobayashi metrics on strongly pseudoconvex domains

Harish Seshadri (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let Ω 1 and Ω 2 be strongly pseudoconvex domains in ℂ n and f : Ω 1 → Ω 2 an isometry for the Kobayashi or Carathéodory metrics. Suppose that f extends as a C 1 map to Ω ¯ 1 . We then prove that f | ∂ Ω 1 : ∂ Ω 1 → ∂ Ω 2 is a CR or anti-CR diffeomorphism. It follows that Ω 1 and Ω 2 must be biholomorphic or anti-biholomorphic.

On isometries of the Kobayashi and Carathéodory metrics

Prachi Mahajan (2012)

Annales Polonici Mathematici

This article considers C¹-smooth isometries of the Kobayashi and Carathéodory metrics on domains in ℂⁿ and the extent to which they behave like holomorphic mappings. First we provide an example which suggests that 𝔹ⁿ cannot be mapped isometrically onto a product domain. In addition, we prove several results on continuous extension of C⁰-isometries f : D₁ → D₂ to the closures under purely local assumptions on the boundaries. As an application, we show that there is no C⁰-isometry between a strongly...

On iterations of Green type integrals for matrix factorizations of the Laplace operator

Alexandre A. Shlapunov (1994)

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

Convergence of special Green integrals for matrix factorization of the Laplace operator in R n is proved. Explicit formulae for solutions of ∂ ¯ -equation in strictly pseudo-convex domains in C n are obtained.

Currently displaying 161 – 180 of 607