Geometry associated with the SL(3,R) action on homogeneous space using the Erlangen program

Abstract

We investigate the action of the Lie group SL(3,R) on the two-dimensional homogeneous space. All the one-parameter subgroups (up to conjugacy) of SL(3,R) are considered. We discuss the orbits and curvatures of these one-parameter subgroups. We also classify these subgroups in terms of fixed points.