Geometry Associated with the SL(3, R) Action on Homogeneous Space Using the Erlangen Program.

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. [ABSTRACT FROM AUTHOR]