Integrable Discrete Nets in Grassmannians

被引：4

作者：

Adler, Vsevolod Eduardovich ^{[1
,2
]}

Bobenko, Alexander Ivanovich ^{[2
]}

Suris, Yuri Borisovich ^{[2
]}

机构：

[1] LD Landau Theoret Phys Inst, Chernogolovka 142432, Russia

[2] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany

来源：

LETTERS IN MATHEMATICAL PHYSICS | 2009年 / 89卷 / 02期

关键词：

discrete differential geometry; multidimensional consistency; Grassmannian; noncommutative Darboux system; QUADRILATERAL LATTICES; GEOMETRY; SURFACES; DARBOUX;

D O I：

10.1007/s11005-009-0328-1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider discrete nets in Grassmannians G(r)(d), which generalize Q-nets ( maps Z(N) -> P(d) with planar elementary quadrilaterals) and Darboux nets (P(d) -valued maps defined on the edges of 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.

引用

页码：131 / 139

页数：9

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