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In this paper, we have investigated the projective action of the Lie group SL(3;R) on the homogeneous space RP2. In particular, we have studied the action of the subgroups of SL(3;R) on the non-degenerate conics in the space RP2. 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. [ABSTRACT FROM AUTHOR]

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]