Geometry associated with the $\text{SL}(3,\mathbb{R})$ action on homogeneous space using the Erlangen program
DOI:
https://doi.org/10.52737/18291163-2022.14.11-1-15Keywords:
Lie Group $\text{SL}(3,\mathbb{R})$, Homogeneous Space, Iwasawa Decomposition, One-Parameter Subgroups, Group Action, Derived Representation, Orbit, Curvature, Fixed PointAbstract
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.
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