We construct a family of (2, n)-almost Grassmannian structures of regularity C1, each admitting a one-parameter group of strongly essential automorphisms, and each not flat on any open set containing the higher-order fixed point in its closure. This shows that Theorem 1.3 of  does not hold assuming only C1 regularity of the structure (see also [3, Prop. 3.5]).
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Both authors wish to thank Katharina Neusser for helpful conversations and an anonymous referee for helpful comments. Melnick gratefully acknowledges support from NSF grant DMS 1255462 and from the Max-Planck-Institut für Mathematik in Bonn, where she was a Visiting Scientist during much of the writing of this paper.
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ČAP, A., MELNICK, K. C1 DEFORMATIONS OF ALMOST GRASSMANNIAN STRUCTURES WITH STRONGLY ESSENTIAL SYMMETRY. Transformation Groups (2020). https://doi.org/10.1007/s00031-020-09584-2