The Bäcklund Transform of Principal Contact Element Nets

Abstract

We investigate geometric aspects of the the Bäcklund transform of principal contact element nets. A Bäcklund transform exists if and only if it the principal contact element net is of constant negative Gaussian curvature (a pseudosphere). We describe an elementary construction of the Bäcklund transform and prove its correctness. Finally, we show that Bianchi's Permutation Theorem remains valid in our discrete setting.

arXiv commentMinor corrections and clarifications

References in corpus (3)

• On organizing principles of Discrete Differential Geometry. Geometry of spheres
• Contributions to Four-Position Theory with Relative Rotations
• Discrete Gliding Along Principal Curves