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Natural Science, Biology, 2024, 14, 67–75
DOI: 10.xxxx/example-doi Special Issue 1(2), 2022 186–1928

Geometry associated with the SL ( 3 , R ) action on homogeneous space using the Erlangen program

Received N/A; revised N/A; accepted N/A
CC BY-NC 4.0 This work is licensed under Creative Commons Attribution–NonCommercial International License (CC BY-NC 4.0).

We investigate the action of the Lie group SL(3,R)SL(3,R) on the two-dimensional homogeneous space. All the one-parameter subgroups (up to conjugacy) of SL(3,R)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.

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