A note on the first-order flexes of smooth surfaces which are tangent to the set of all nonrigid surfaces

TL;DR

This paper proves that certain first-order flexes of smooth surfaces in 3D space, tangent to nonrigid surfaces, can be extended to second-order flexes, advancing understanding of surface flexibility.

Contribution

It establishes a theoretical extension from first-order to second-order flexes for specific smooth surfaces in Euclidean space.

Findings

First-order flexes tangent to nonrigid surfaces can be extended to second-order flexes.

Provides a mathematical foundation for surface flexibility analysis.

Enhances understanding of deformation properties of smooth surfaces.

Abstract

We prove that first-order flexes of smooth surfaces in Euclidean 3-space, which are tangent to the set of all nonrigid surfaces, can be extended to second-order flexes.