On a quaternionic analogue of the cross-ratio

DOI10.1007/s00006-012-0325-9zbMath1257.15014arXiv1112.0612OpenAlexW2085784518MaRDI QIDQ691051

Matvei Libine, Ewain Gwynne

Publication date: 29 November 2012

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.0612

zbMATH Keywords

Möbius transformationsquaternionsconformal transformationscross-ratioMöbius geometryfractional linear transformations

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Clifford algebras, spinors (15A66) Linear transformations, semilinear transformations (15A04) Möbius geometries (51B10)

Related Items (11)

Geometry of Riccati equations over normed division algebras ⋮ Möbius transformation for left-derivative quaternion holomorphic functions ⋮ Projective cross-ratio on hypercomplex numbers ⋮ Quaternionic hyperbolic Fenchel-Nielsen coordinates ⋮ Cross-ratios and the Ptolemaean inequality in boundaries of symmetric spaces of rank 1 ⋮ Projective compactification of \(\mathbb R^{1,1}\) and its Möbius geometry ⋮ Low-dimensional dynamics in non-Abelian Kuramoto model on the 3-sphere ⋮ Spectrahedral cones generated by rank \(1\) matrices ⋮ Geometric properties of conformal transformations on \(\mathbb R^{p,q}\) ⋮ Configurations of flags in orbits of real forms ⋮ On the classification of right-angled hyperbolic hexagons in dimension 5

Cites Work

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• Quaternionic analysis, representation theory and physics
• The cross ratio and Clifford algebras
• A discrete version of the Darboux transform for isothermic surfaces
• Discrete isothermic surfaces.
• Moebius transformations and the Poincare distance in the quaternionic setting
• Conformal geometry of surfaces in \(S^4\) and quaternions

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