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Strongly essential flows on irreducible parabolic geometries


Authors: Karin Melnick and Katharina Neusser
Journal: Trans. Amer. Math. Soc. 368 (2016), 8079-8110
MSC (2010): Primary 53B15; Secondary 37C10
DOI: https://doi.org/10.1090/tran/6814
Published electronically: April 15, 2016
MathSciNet review: 3546794
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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.


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Additional Information

Karin Melnick
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email: karin@math.umd.edu

Katharina Neusser
Affiliation: Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200, Australia
Address at time of publication: Mathematical Institute, Charles University, Sokolovská 83, Praha, Czech Republic
Email: Katharina.neusser@anu.edu.au, kath.neusser@gmail.com

DOI: https://doi.org/10.1090/tran/6814
Received by editor(s): January 13, 2015
Received by editor(s) in revised form: May 7, 2015
Published electronically: April 15, 2016
Additional Notes: The first author was partially supported during work on this project by a Centennial Fellowship from the American Mathematical Society and by NSF grants DMS-1007136 and 1255462
Article copyright: © Copyright 2016 American Mathematical Society