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Deformations of G2 and Spin(7) Structures

Published online by Cambridge University Press:  20 November 2018

Spiro Karigiannis
Spiro Karigiannis*
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, email: spiro@math.mcmaster.ca
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Abstract

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We consider some deformations of ${{G}_{2}}$-structures on 7-manifolds. We discover a canonical way to deform a ${{G}_{2}}$-structure by a vector field in which the associated metric gets “twisted” in some way by the vector cross product. We present a system of partial differential equations for an unknown vector field $w$ whose solution would yield a manifold with holonomy ${{G}_{2}}$. Similarly we consider analogous constructions for Spin(7)-structures on 8-manifolds. Some of the results carry over directly, while others do not because of the increased complexity of the Spin(7) case.

Keywords

53C2653C29G2 Spin(7)holonomymetricscross product
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 57 , Issue 5 , 01 October 2005 , pp. 1012 - 1055
Copyright
Copyright © Canadian Mathematical Society 2005

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