The Geometry of the Projective Action of SL(3,R) from the Erlangen Perspective - Biswas, Debapriya; Rajwar, Ipsita (Armenian Journal of Mathematics, 2024)
In this paper, we have investigated the projective action of the Lie group SL(3,R) on the homogeneous space RP^2. In particular, we have studied the action of the subgroups of SL(3,R) on the non-degenerate conics in the space RP^2. Using the Iwasawa decomposition of SL(2,R), we demonstrate that the isotropy subgroup of the projective unit circle is isomorphic to PSL(2,R) under certain conditions.