Notes in the isometric deformations problem in codimension 2

2023/12/03 by Guajardo, Diego
#53B25 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.01254

Abstract

We present a discussion about the local isometric rigidity problem in codimension 2 with a concrete example. We show the necessity of extending the notions of genuine and honest rigidity in order to have the transitivity property. In order to do so, we show the necessity of studying the isometric immersions in semi-Euclidean spaces. We show that this extension comes with a natural type of singularity in the inner product.

Related

• Isometric rigidity in codimension two
• Convexity, Rigidity, and Reduction of Codimension of Isometric Immersions into Space Forms
• Euclidean hypersurfaces with genuine deformations in codimension two
• First cohomology, rigidity and deformations of isometric group actions
• Isometric Euclidean submanifolds with isometric Gauss maps