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Register a new userCircle complexes and the discrete CKP equation
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Added by
Alexander I. Bobenko
Publication date
2015
fields
Physics
and research's language is
English
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In the spirit of Kleins Erlangen Program, we investigate the geometric and algebraic structure of fundamental line complexes and the underlying privileged discrete integrable system for the minors of a matrix which constitute associated Plucker coordinates. Particular emphasis is put on the restriction to Lie circle geometry which is intimately related to the master dCKP equation of discrete integrable systems theory. The geometric interpretation, construction and integrability of fundamental line complexes in Mobius, Laguerre and hyperbolic geometry are discussed in detail. In the process, we encounter various avatars of classical and novel incidence theorems and associated cross- and multi-ratio identities for particular hypercomplex numbers. This leads to a discrete integrable equation which, in the context of Mobius geometry, governs novel doubly hexagonal circle patterns.
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