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 \'E. Cartan. As a consequence one obtains a characterization of all naturally reductive left-invariant Riemannian metrics of $\,SL(2,\R)$.
Iannuzzi, A., Halverscheid, S. (2006). On Naturally reductive left-invariant metrics of SL(2,R). ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE, 5, 171-187.
On Naturally reductive left-invariant metrics of SL(2,R)
IANNUZZI, ANDREA;
2006-01-01
Abstract
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 \'E. Cartan. As a consequence one obtains a characterization of all naturally reductive left-invariant Riemannian metrics of $\,SL(2,\R)$.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
