On isometric correspondence of leaves

Abstract

We prove that for a generic $3$-dimensional integrable rolling distribution of contact elements (excluding developable seed and isotropic developable leaves) isometric correspondence of leaves of a general nature (independent of the shape of the seed) requires the Bäcklund transformation.

arXiv admin note: substantial text overlap with arXiv:1212.2326, arXiv:1110.5474; proof of the main theorem is incomplete

References in corpus (1)

• On Bianchi's Backlund transformation of quadrics