# C^1 Deformations of almost-Grassmannian structures with strongly essential symmetry

## TL;DR

This paper constructs specific $C^1$ almost Grassmannian structures with strongly essential automorphisms, demonstrating limitations of a previous theorem under low regularity assumptions.

## Contribution

It provides explicit examples of $C^1$ structures with strongly essential symmetries, showing that certain flatness results do not hold at this regularity level.

## Key findings

- Existence of $C^1$ almost Grassmannian structures with strongly essential automorphisms
- These structures are not flat near higher-order fixed points
- Counterexamples to previous flatness theorems at $C^1$ regularity

## Abstract

We construct a family of $(2,n)$-almost Grassmannian structures of regularity $C^1$, each admitting a one-parameter group of strongly essential automorphisms, and each not flat on any neighborhood of the higher-order fixed point. This shows that Theorem 1.3 of [9] does not hold assuming only $C^1$ regularity of the structure (see also [2, Prop 3.5]).