Integrable discrete nets in Grassmannians

Vsevolod Eduardovich Adler, Alexander Ivanovich Bobenko, Yuri Borisovich Suris

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We consider discrete nets in Grassmannians, rd, which generalize Q-nets (maps N ← ℙd with planar elementary quadrilaterals) and Darboux nets (ℙd-valued maps defined on the edges of ℤN 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.

Original languageEnglish
Pages (from-to)131-139
Number of pages9
JournalLetters in Mathematical Physics
Volume89
Issue number2
DOIs
StatePublished - Aug 2009
Externally publishedYes

Keywords

  • Discrete differential geometry
  • Grassmannian
  • Multidimensional consistency
  • Noncommutative Darboux system

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