On naturally reductive left-invariant metrics of SL(2,ℝ)
2006 | journal article
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Details
- Authors
- Halverscheid, Stefan ; Iannuzzi, Andrea
- 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 É. Cartan. As a consequence one obtains a characterization of all naturally reductive left-invariant Riemannian metrics of SL(2, ℝ).
- Issue Date
- 2006
- Journal
- Applied Mathematics Letters
- Language
- English