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We consider some deformations of
-structures on 7-manifolds. We discover a canonical way to deform a
-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
. 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.
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