Integrable Discrete Nets in Grassmannians
Abstract
We consider discrete nets in Grassmannians {mathbb{G}^{d}_{r}}, which generalize Qnets (maps {mathbb{Z}^Ntomathbb{P}^d} with planar elementary quadrilaterals) and Darboux nets ({mathbb{P}^d}valued maps defined on the edges of {mathbb{Z}^N} such that quadruples of points corresponding to elementary squares are all collinear). We give a geometric proof of integrability (multidimensional consistency) of these novel nets, and show that they are analytically described by the noncommutative discrete Darboux system.
 Publication:

Letters in Mathematical Physics
 Pub Date:
 August 2009
 DOI:
 10.1007/s1100500903281
 arXiv:
 arXiv:0812.5102
 Bibcode:
 2009LMaPh..89..131A
 Keywords:

 Mathematics  Differential Geometry;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 10 pp