Clifford lattices and a conformal generalization of Desargues' theorem

Alastair D King; Wolfgang K Schief

doi:10.1016/j.geomphys.2011.12.009

Clifford lattices and a conformal generalization of Desargues' theorem

Alastair D King, Wolfgang K Schief

Department of Mathematical Sciences

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Abstract

Lattices composed of Clifford point–circle configurations provide a geometric representation of the discrete Schwarzian KP (dSKP) equation. Based on an An perspective on such lattices, it is shown that their integrability, and hence that of the dSKP equation, is a consequence of a conformal generalization of the classical Desargues theorem of projective geometry.

Original language	English
Pages (from-to)	1088-1096
Number of pages	9
Journal	Journal of Geometry and Physics
Volume	62
Issue number	5
Early online date	30 Dec 2011
DOIs	https://doi.org/10.1016/j.geomphys.2011.12.009
Publication status	Published - May 2012

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King_JGP_2012_62_5_1088.pdf
NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Geometry and Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Geometry and Physics, vol 62, issue 5, 2012, DOI 10.1016/j.geomphys.2011.12.009
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abstract = "Lattices composed of Clifford point–circle configurations provide a geometric representation of the discrete Schwarzian KP (dSKP) equation. Based on an An perspective on such lattices, it is shown that their integrability, and hence that of the dSKP equation, is a consequence of a conformal generalization of the classical Desargues theorem of projective geometry.",

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AB - Lattices composed of Clifford point–circle configurations provide a geometric representation of the discrete Schwarzian KP (dSKP) equation. Based on an An perspective on such lattices, it is shown that their integrability, and hence that of the dSKP equation, is a consequence of a conformal generalization of the classical Desargues theorem of projective geometry.

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Clifford lattices and a conformal generalization of Desargues' theorem

Abstract

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