Conformal deformations preserving the Gauss map

Enaldo Vergasta

Vol. 156 (1992), No. 2, 359–369

DOI: 10.2140/pjm.1992.156.359

Abstract

In this work, given a conformal immersion f : Mⁿ → ℝ^N of a Riemannian manifold Mⁿ into a euclidean space ℝ^N, we establish conditions for the existence of another conformal immersion f : Mⁿ → ℝ^N with the same Gauss map as f. In particular, for n = 2 and N = 3, these conditions are described by means of a partial differential equation on the principal curvatures of f.

Mathematical Subject Classification 2000

Primary: 53C42

Secondary: 53A30

Milestones

Received: 2 May 1988

Revised: 25 August 1991

Published: 1 December 1992