Isometric rigidity in codimension two

TL;DR

This paper proves that certain rank-two, parabolic, nonruled Euclidean submanifolds with codimension two are isometrically rigid and provides a parametric classification of all such submanifolds.

Contribution

It generalizes previous rigidity results and offers a comprehensive parametric classification of parabolic submanifolds in codimension two.

Findings

Rank-two, parabolic, nonruled submanifolds are isometrically rigid.

Provides a parametric classification of all parabolic submanifolds.

Extends known rigidity results to a broader class of submanifolds.

Abstract

We show that among the Euclidean submanifolds with codimension two the ones of rank two that are parabolic but nonruled are isometrically rigid. This generalizes the result in [10] that these submanifolds are genuinely rigid. In addition, we give a parametric classifications of all parabolic submanifolds.