Analog of selfduality in dimension nine

Anna Fino; Paweł Nurowski

doi:10.1515/crelle-2013-0010

Published by De Gruyter April 9, 2013

Analog of selfduality in dimension nine

Anna Fino and Paweł Nurowski

From the journal Journal für die reine und angewandte Mathematik (Crelles Journal)

https://doi.org/10.1515/crelle-2013-0010

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Abstract

We introduce a type of Riemannian geometry in nine dimensions, which can be viewed as the counterpart of selfduality in four dimensions. This geometry is related to a 9-dimensional irreducible representation of SO(3)×SO(3) and it turns out to be defined by a differential 4-form. Structures admitting a metric connection with totally antisymmetric torsion and preserving the 4-form are studied in detail, producing locally homogeneous examples which can be viewed as analogs of self-dual 4-manifolds in dimension nine.

Funding source: Polish Ministry of Research and Higher Education

Award Identifier / Grant number: NN201 607540, NN202 104838

Funding source: MIUR

Award Identifier / Grant number: Differential Geometry and Global Analysis (PRIN07)

Funding source: Indam

Award Identifier / Grant number: GNSAGA

We would like to thank Robert Bryant, Antonio Di Scala, Boris Doubrov, Mike Eastwood, Katja Sagerschnig and Simon Salamon for useful comments and suggestions.

Received: 2011-9-13

Revised: 2013-1-17

Published Online: 2013-4-9

Published in Print: 2015-2-1

Analog of selfduality in dimension nine

Abstract

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