Geometry associated with the $\text{SL}(3,\mathbb{R})$ action on homogeneous space using the Erlangen program - Biswas, Debapriya; Rajwar, Ipsita (Armenian Journal of Mathematics, 2022)
We investigate the action of the Lie group $\text{SL}(3,\mathbb{R})$ on the two-dimensional homogeneous space. All the one-parameter subgroups (up to conjugacy) of $\text{SL}(3,\mathbb{R})$ are considered. We discuss the orbits and curvatures of these one-parameter subgroups. We also classify these subgroups in terms of fixed points.
Keywords: Lie Group $\text{SL}(3,\mathbb{R})$; Homogeneous Space; Iwasawa Decomposition; One-Parameter Subgroups; Group Action; Derived Representation; Orbit; Curvature; Fixed Point