Strongly essential flows on irreducible parabolic geometries
Abstract
We study the local geometry of irreducible parabolic geometries admitting strongly essential flows; these are flows by local automorphisms with higher-order fixed points. We prove several new rigidity results, and recover some old ones for projective and conformal structures, which show that in many cases the existence of a strongly essential flow implies local flatness of the geometry on an open set having the fixed point in its closure. For almost c-projective and almost quaternionic structures we can moreover show flatness of the geometry on a neighborhood of the fixed point.
Keywords
Cite
@article{arxiv.1410.4647,
title = {Strongly essential flows on irreducible parabolic geometries},
author = {Karin Melnick and Katharina Neusser},
journal= {arXiv preprint arXiv:1410.4647},
year = {2015}
}
Comments
34 pages. Proof of Proposition 3.1 significantly shortened, under slightly less general hypotheses (see Remark 3.1). Typos corrected and references updated. To appear in Transactions of the AMS