An axiomatic foundation of Cayley-Klein geometries

DOI10.1007/s00022-015-0293-zzbMath1360.51006OpenAlexW2126121697MaRDI QIDQ506923

Rolf Struve

Publication date: 2 February 2017

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00022-015-0293-z

zbMATH Keywords

non-Euclidean geometryCayley-Klein geometrycalculus of reflections

Mathematics Subject Classification ID

Absolute planes in metric geometry (51F05) Reflection groups, reflection geometries (51F15)

Related Items (9)

A theory of duality in Euclidean geometry ⋮ Metric Geometries in an Axiomatic Perspective ⋮ The Axiomatic Destiny of the Theorems of Pappus and Desargues ⋮ A universal linear algebraic model for conformal geometries ⋮ The Thomsen-Bachmann correspondence in metric geometry. I ⋮ The Thomsen-Bachmann correspondence in metric geometry. II ⋮ The principle of duality in Euclidean and in absolute geometry ⋮ Absolute isotropic geometry ⋮ An axiomatic analysis of the Droz-Farny line theorem

Cites Work

• Non-euclidean geometries: the Cayley-Klein approach
• Ein spiegelungsgeometrischer Aufbau der Galileischen Geometrie
• Groups and plane geometry
• On M. T. Calapso's characterization of the metric of an absolute plane
• Ein spiegelungsgeometrischer Aufbau der cominkowskischen Geometrie
• Coeuklidische Hjelmslevgruppen. (On co-Euclidean Hjelmslev groups)
• Projective spaces with Cayley-Klein metrics
• Minkowskische und absolute Geometrie. I, II
• Eine Synthetische Charakterisierung der Cayley‐Kleinschen Geometrien
• Zum Begriff Der Projektiv-Metrischen Ebene
• Towards a Unified Approach for Proving Geometric Ergodicity and Mixing Properties of Nonlinear Autoregressive Processes
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