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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 ′ .

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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