# The infinitesimally bendable Euclidean hypersurfaces

## TL;DR

This paper completes the classification of nonflat infinitesimally bendable hypersurfaces in Euclidean space, building on Sbrana's work from 1909, and provides a comprehensive local characterization.

## Contribution

It finalizes the local classification of these hypersurfaces, extending and completing Sbrana's 1909 foundational work.

## Key findings

- Complete local classification of nonflat infinitesimally bendable hypersurfaces
- Extension of Sbrana's 1909 work
- New geometric characterizations and descriptions

## Abstract

The main purpose of this paper is to complete the work initiated by Sbrana in 1909 giving a complete local classification of the nonflat infinitesimally bendable hypersurfaces in Euclidean space.