Displaying similar documents to “On discrete subgroups of Lie groups and elliptic geometric structures.”

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

Stefan Halverscheid, Andrea Iannuzzi (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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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...