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

Author(s)

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

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.

DOI: 10.52737/18291163-2022.14.11-1-15 Armenian Journal of Mathematics, 14(11) 1-15

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Keywords

Lie Group SL ( 3 , R ) , Homogeneous Space, Iwasawa Decomposition, One-Parameter Subgroups, Group Action, Derived Representation, Orbit, Curvature, Fixed Point

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