Isometric deformation of surfaces in R³ preserving the mean curvature function

A. Gervasio Colares and Katsuei Kenmotsu

Vol. 136 (1989), No. 1, 71–80

DOI: 10.2140/pjm.1989.136.71

Abstract

The purpose of this paper is to classify surfaces in Euclidean 3-space with constant Gaussian curvature which admit non-trivial one-parameter families of isometric immersions preserving the mean curvature function. It is shown that the Gaussian curvature must be zero and, if the mean curvature is not constant, then such isometric immersions are some deformations of the cylinder over a logarithmic spiral.

Mathematical Subject Classification 2000

Primary: 53A10

Milestones

Received: 21 April 1987

Published: 1 January 1989