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On isometric correspondence of leaves

Ion I. Dinca

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.

On isometric correspondence of leaves

Abstract

We prove that for a generic -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.

Paper Structure

This paper contains 5 sections, 1 theorem, 137 equations.

Table of Contents

  1. Introduction
  2. The rolling problem for surfaces
  3. Proof of Theorem \ref{['th:th1']}
  4. The case $m=V\times N_0+\mathbf{m}N_0+\mathbf{n}V$
  5. The case $m=V+\mathbf{m}N_0$

Key Result

theorem \oldthetheorem

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.

Theorems & Definitions (4)

  • Definition \oldthetheorem
  • Definition \oldthetheorem
  • Definition \oldthetheorem
  • theorem \oldthetheorem