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Deformations of G_2 and Spin(7) Structures on Manifolds

Spiro Karigiannis
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Abstract

We consider some infinitesmal and global 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 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 non-linearity of the Spin(7) case.

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Spiro Karigiannis. 2003-01-20. Deformations of G_2 and Spin(7) Structures on Manifolds. https://doi.org/10.4153/cjm-2005-039-x

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