Euclidean hypersurfaces with genuine deformations in codimension two

Author(s)

Dajczer, M. ^[1] ; Florit, L. ^[1] ; Tojeiro, R. ^[2]

Affiliation

^[1] IMPA, BR-22460320 Rio De Janeiro - Brazil

^[2] Univ Fed Sao Carlos, BR-13565905 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: MANUSCRIPTA MATHEMATICA; v. 140, n. 3-4, p. 621-643, MAR 2013.
• Web of Science Citations: 3

Abstract

We classify hypersurfaces of rank two of Euclidean space Rn+1 that admit genuine isometric deformations in Rn+2. That an isometric immersion (f) over cap : M-n -> Rn+2 is a genuine isometric deformation of a hypersurface f : M-n -> Rn+1 means that (f) over cap is nowhere a composition (f) over cap = (f) over cap circle f, where (f) over cap : V subset of Rn+1 -> Rn+2 is an isometric immersion of an open subset V containing the hypersurface. (AU)

• FAPESP's process: 07/03192-7 - Submanifold geometry and Morse theory in finite and infinite dimensions
• Grantee: Claudio Gorodski
• Support Opportunities: Research Projects - Thematic Grants