On a new definition of the Bäcklund transformation in the isometric deformation of surfaces

Abstract

We prove that a generic $4$-dimensional integrable rolling distribution of contact elements with the symmetry of the tangency configuration (excluding developable seed and isotropic developable leaves) splits into an $1$-dimensional family of generic $3$-dimensional integrable rolling distributions of contact elements with the symmetry of the tangency configuration, thus introducing a new definition of the Bäcklund transformation in the isometric deformation of surfaces.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1212.2326, arXiv:1907.13483, arXiv:1110.5474