Skip Navigation



The Quarterly Journal of Mathematics Advance Access published online on July 14, 2008
The Quarterly Journal of Mathematics, doi:10.1093/qmath/han020
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Karigiannis, S.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2008. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

FLOWS OF G2-STRUCTURES, I

Spiro Karigiannis{dagger}

Mathematical Institute, University of Oxford, 24-29 St. Giles, Oxford OX1 3LB, UK

{dagger} E-mail: karigiannis{at}maths.ox.ac.uk

Received 12 October 2007; revised 6 May 2008
  Abstract

This is a foundational paper on flows of G2-structures. We use local coordinates to describe the four torsion forms of a G2 and derive the evolution equations for a general flow of a G2-structure {varphi} on a 7-manifold M. Specifically, we compute the evolution of the metric g, the dual 4-form {psi} and the four independent torsion forms. In the process we obtain a simple new proof of a theorem of Fernández–Gray.

As an application of our evolution equations, we derive an analogue of the second Bianchi identity in G2-geometry which appears to be new, at least in this form. We use this result to derive explicit formulas for the Ricci tensor and part of the Riemann curvature tensor in terms of the torsion. These in turn lead to new proofs of several known results in G2-geometry.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.