The Geometry of the Projective Action of $\text{SL}(3,\mathbb{R})$ from the Erlangen Perspective

DOI10.52737/18291163-2024.16.1-1-28OpenAlexW4390765551MaRDI QIDQ6201826

Unnamed Author, Debapriya Biswas

Publication date: 26 March 2024

Published in: Armenian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.52737/18291163-2024.16.1-1-28

zbMATH Keywords

real hyperbolic motion group

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Semisimple Lie groups and their representations (22E46) General properties and structure of real Lie groups (22E15) Topological linear incidence structures (51H10)

Cites Work

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• The invariance of cycles in upper half plane under Möbius transformation in EPH cases
• Erlangen program at large-1: geometry of invariants
• The actions of subgroups of \(SL_2(\mathbb R)\) for the Clifford algebra in EPH cases
• Projective cross-ratio on hypercomplex numbers
• Möbius action of \(\mathrm{SL}(2; \mathbb{R})\) on different homogeneous spaces
• Projective coordinates and compactification in elliptic, parabolic and hyperbolic 2-D geometry
• Perspectives on Projective Geometry
• Geometry of Möbius Transformations
• SL(2,R) Actions on Surfaces
• Small Subgroups of
• Geometric Invariants Under the Möbius Action of the Group SL(2;R)
• Geometry associated with the $\text{SL}(3,\mathbb{R})$ action on homogeneous space using the Erlangen program
• Some model theory of SL(2,R)
• Poincaré extension of Möbius transformations
• Isometric action of \(SL_{2}(\mathbb{R})\) on homogeneous spaces
• Invariant projective properties under the action of the Lie group \(\mathrm{SL}(3; \mathbb{R})\) on \(\mathbb{RP}^2\)

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