Some Results On The Infinitesimal Bending And The Bonnet Problem

Abstract

The infinitesimal bending problem and the Bonnet problem are investigated together. The conditions for a surface and its infinitesimal deformation surface to be a Bonnet pair are examined. It is shown that Bonnet pairs which can be infinitesimally bending of each other, are only the isothermic Bonnet surfaces; and the relation of the geodesic torsions of the A-net and Bonnet net of them is determined as t = 2 (t) over bar (e) and it is found that their associate surface is also an isothermic surface.