Jump to ContentJump to Main Navigation
Show Summary Details

Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

12 Issues per year


IMPACT FACTOR increased in 2015: 1.616
5-year IMPACT FACTOR: 1.690
Rank 18 out of 312 in category Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2015: 3.614
Source Normalized Impact per Paper (SNIP) 2015: 1.901
Impact per Publication (IPP) 2015: 1.302

Mathematical Citation Quotient (MCQ) 2015: 1.53

Online
ISSN
1435-5345
See all formats and pricing
Select Volume and Issue

Issues

On the irreducibility of locally metric connections

Florin Belgun
  • Fachbereich Mathematik, Bereich AD, Hamburg University, Bundesstr. 55 (Geomatikum), 20146 Hamburg, Germany
  • :
/ Andrei Moroianu
  • Laboratoire de Mathématiques, Université de Versailles-St Quentin, UMR 8100 du CNRS, 45 avenue des États-Unis, 78035 Versailles, France
  • :
Published Online: 2014-01-05 | DOI: https://doi.org/10.1515/crelle-2013-0128

Abstract

A locally metric connection on a smooth manifold M is a torsion-free connection D on TM with compact restricted holonomy group Hol 0(D). If the holonomy representation of such a connection is irreducible, then D preserves a conformal structure on M. Under some natural geometric assumption on the life-time of incomplete geodesics, we prove that conversely, a locally metric connection D preserving a conformal structure on a compact manifold M has irreducible holonomy representation, unless Hol 0(D)=0 or D is the Levi-Civita connection of a Riemannian metric on M. This result generalizes Gallot's theorem on the irreducibility of Riemannian cones to a much wider class of connections. As an application, we give the geometric description of compact conformal manifolds carrying a tame closed Weyl connection with non-generic holonomy.


Received: 2012-04-13

Revised: 2013-10-29

Published Online: 2014-01-05

Published in Print: 2016-05-01


Funding Source: Agence Nationale de la Recherche

Award identifier / Grant number: ANR-10-BLAN 0105


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2016, Issue 714, Pages 123–150, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2013-0128, January 2014

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Vladimir S. Matveev and Yuri Nikolayevsky
Comptes Rendus Mathematique, 2015, Volume 353, Number 5, Page 455

Comments (0)

Please log in or register to comment.