Showing papers by "Wolfgang K. Schief published in 2008"

On the Integrability of Infinitesimal and Finite Deformations of Polyhedral Surfaces

Abstract: It is established that there exists an intimate connection between isometric deformations of polyhedral surfaces and discrete integrable systems. In particular, Sauer’s kinematic approach is adopted to show that second-order infinitesimal isometric deformations of discrete surfaces composed of planar quadrilaterals (discrete conjugate nets) are determined by the solutions of an integrable discrete version of Bianchi’s classical equation governing finite isometric deformations of conjugate nets. Moreover, it is demonstrated that finite isometric deformations of discrete conjugate nets are completely encapsulated in the standard integrable discretization of a particular nonlinear σ-model subject to a constraint. The deformability of discrete Voss surfaces is thereby retrieved in a natural manner.

A novel generalization of Clifford's classical point-circle configuration. Geometric interpretation of the quaternionic discrete Schwarzian KP equation

Abstract: The algebraic and geometric properties of a novel generalization of Clifford's classical C4 point-circle configuration are analysed. A connection with the integrable quaternionic discrete Schwarzian Kadomtsev-Petviashvili equation is revealed.