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Balls for the Kobayashi distance and extension of the automorphisms of strictly convex domains in $C^{n}$ with real analytic boundary

Andrea Iannuzzi — 1994

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

It is shown that given a bounded strictly convex domain $Ω$ in $C^{n}$ with real analitic boundary and a point $x_{0}$ in $Ω$ , there exists a larger bounded strictly convex domain $Ω^{'}$ with real analitic boundary, close as wished to $Ω$ , such that $Ω$ is a ball for the Kobayashi distance of $Ω^{'}$ with center $x_{0}$ . The result is applied to prove that if $Ω$ is not biholomorphic to the ball then any automorphism of $Ω$ extends to an automorphism of $Ω^{'}$ .

[unknown]

Laura Geatti; Andrea Iannuzzi

Annales de l’institut Fourier

On naturally reductive left-invariant metrics of $SL (2, ℝ)$

Stefan Halverscheid; Andrea Iannuzzi — 2006

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On any real semisimple Lie group we consider a one-parameter family of left-invariant naturally reductive metrics. Their geodesic flow in terms of Killing curves, the Levi Civita connection and the main curvature properties are explicitly computed. Furthermore we present a group theoretical revisitation of a classical realization of all simply connected 3-dimensional manifolds with a transitive group of isometries due to L. Bianchi and É. Cartan. As a consequence one obtains a characterization of...

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Currently displaying 1 – 3 of 3

Balls for the Kobayashi distance and extension of the automorphisms of strictly convex domains in C n with real analytic boundary

[unknown]

On naturally reductive left-invariant metrics of SL ( 2 , ℝ )

Balls for the Kobayashi distance and extension of the automorphisms of strictly convex domains in $C^{n}$ with real analytic boundary

On naturally reductive left-invariant metrics of $SL (2, ℝ)$