Codimension two isometric immersions between Euclidean spaces

Lee Barlow Whitt

Vol. 119 (1985), No. 2, 481–487

DOI: 10.2140/pjm.1985.119.481

Abstract

Hartman and Nirenberg showed that any C^∞ isometric immersion f : Eⁿ → Eⁿ⁺¹ between flat Euclidean spaces is a cylinder erected over a plane curve. We show that in the codimension two case, f : Eⁿ → Eⁿ⁺² factors as a composition of isometric immersions f = f₁ ∘ f₂ : Eⁿ → Eⁿ⁺¹ → Eⁿ⁺², when n > 1 and f has nowhere zero normal curvature. Counterexamples are given if this assumption is relaxed.

Mathematical Subject Classification 2000

Primary: 53C42

Secondary: 53A07

Milestones

Received: 17 February 1982

Revised: 22 January 1985

Published: 1 October 1985