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

Author(s)

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

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.

DOI: 10.52737/18291163-2024.16.1-1-28 Armenian Journal of Mathematics, 16(1) 1-28

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Keywords

Lie Group SL(3,R), Homogeneous Space, Conics, Exponential Map, Iwasawa Decomposition

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