Strongly essential flows on irreducible parabolic geometries
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- by Karin Melnick and Katharina Neusser PDF
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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.References
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Additional Information
- Karin Melnick
- Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
- MR Author ID: 819221
- 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
- MR Author ID: 883746
- Email: Katharina.neusser@anu.edu.au, kath.neusser@gmail.com
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 8079-8110
- MSC (2010): Primary 53B15; Secondary 37C10
- DOI: https://doi.org/10.1090/tran/6814
- MathSciNet review: 3546794