Isometric action of SL(2,R) on homogeneous spaces

Details Isometric action of SL(2,R) on homogeneous spaces Isometric action of SL(2,R) on homogeneous spaces

2008-10-02

arxiv.org/abs/0810.0368v3

Mathematics

Metric Geometry

LaTeX, 10 pages, 9 EPS figures

Scientific paper

We investigate the SL(2,R) invariant geodesic curves with the as- sociated invariant distance function in parabolic geometry. Parabolic geom- etry naturally occurs in the study of SL(2,R) and is placed in between the elliptic and the hyperbolic (also known as the Lobachevsky half-plane and 2- dimensional Minkowski half-plane space-time) geometries. Initially we attempt to use standard methods of finding geodesics but they lead to degeneracy in this setup. Instead, by studying closely the two related elliptic and hyperbolic geometries we discover a unified approach to a more exotic and less obvious parabolic case. With aid of common invariants we describe the possible dis- tance functions that turn out to have some unexpected, interesting properties.

Affiliated with

Also associated with

No associations

Rating

Isometric action of SL(2,R) on homogeneous spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Isometric action of SL(2,R) on homogeneous spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Isometric action of SL(2,R) on homogeneous spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-492023