Integrable discrete nets in Grassmannians

Details Integrable discrete nets in Grassmannians Integrable discrete nets in Grassmannians

2008-12-30

arxiv.org/abs/0812.5102v1

Lett. Math. Phys., 2009, 89, No. 2, p. 131-139.

Mathematics

Differential Geometry

10 pp

Scientific paper

We consider discrete nets in Grassmannians $\mathbb{G}^d_r$ which generalize Q-nets (maps $\mathbb{Z}^N\to\mathbb{P}^d$ 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.

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