Geometry of quadrilateral nets: second Hamiltonian form

TL;DR

This paper explores the geometric structure of quadrilateral nets, identifying a second Hamiltonian form within the framework of discrete-differential geometry, expanding understanding of their Hamiltonian properties.

Contribution

It introduces and characterizes a second Hamiltonian form in the geometry of quadrilateral nets, complementing the known first form.

Findings

Identification of a second Hamiltonian form in quadrilateral nets

Extension of discrete-differential geometry framework

Enhanced understanding of Hamiltonian structures in discrete systems

Abstract

Discrete Darboux-Manakov-Zakharov systems possess two distinct Hamiltonian forms. In the framework of discrete-differential geometry one Hamiltonian form appears in a geometry of circular net. In this paper a geometry of second form is identified.