Geometric aspects of Bäcklund transformations of Weingarten submanifolds

Steven Buyske

Vol. 166 (1994), No. 2, 213–223

DOI: 10.2140/pjm.1994.166.213

Abstract

If f₁ and f₂ are immersions of an n-manifold M into R²ⁿ⁻¹ such that their induced frame bundles differ by a constant right action, then f₁ and f₂ both satisfy a Weingarten condition on their normal bundles and the right action corresponds to a generalization of the classical Bäcklund transformation.

Mathematical Subject Classification 2000

Primary: 53A07

Secondary: 58G37

Milestones

Received: 18 August 1992

Revised: 30 November 1992

Accepted: 11 January 1993

Published: 1 December 1994