Displaying similar documents to “On pairs of metrics invariant under a cocompact action of a group.”

Invariant metrics on G -spaces

Bogusław Hajduk, Rafał Walczak (2003)

Czechoslovak Mathematical Journal

Similarity:

Let X be a G -space such that the orbit space X / G is metrizable. Suppose a family of slices is given at each point of X . We study a construction which associates, under some conditions on the family of slices, with any metric on X / G an invariant metric on X . We show also that a family of slices with the required properties exists for any action of a countable group on a locally compact and locally connected metric space.

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

Similarity:

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...