Euclidean hypersurfaces with genuine deformations in codimension two

2010/10/14 by Luis A. Florit, Marcos Dajczer, Florit, Luis +3
Mathematics · Physics and Astronomy · #53B25 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1010.2932

openalex publication_date 2010/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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\colon Mⁿ→\Rⁿ⁺² is a genuine isometric deformation of a hypersurface f\colon Mⁿ→\Rⁿ⁺¹ means that f is nowhere a composition f= F∘ f, where F\colon V⊂ \Rⁿ⁺¹→\Rⁿ⁺² is an isometric immersion of an open subset V containing f(M).

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