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Associative submanifolds  A  in nearly parallel  G  2 -manifolds  Y  are minimal 3-submanifolds in spin 7-manifolds with a real Killing spinor. The Riemannian cone over  Y  has the holonomy group contained in    Spin   (  7  )and the Riemannian cone over  A  is a Cayley submanifold.

Second-Order deformations of associative submanifolds in nearly parallel G 2 -manifolds