The Geometry of the Projective Action of SL ( 3 , R ) from the Erlangen Perspective

Debapriya Biswas

Received N/A; revised N/A; accepted N/A

This work is licensed under Creative Commons Attribution–NonCommercial International License (CC BY-NC 4.0).

In this paper, we have investigated the projective action of the Lie group SL(3,R)SL(3,R) on the homogeneous space RP2RP2. In particular, we have studied the action of the subgroups of SL(3,R)SL(3,R) on the non-degenerate conics in the space RP2RP2. Using the Iwasawa decomposition of SL(2,R)SL(2,R), we demonstrate that the isotropy subgroup of the projective unit circle is isomorphic to PSL(2,R)PSL(2,R) under certain conditions.

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The Geometry of the Projective Action of SL ( 3 , R ) from the Erlangen Perspective

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