On nearly parallel G_2-structures

Abstract : A nearly parallel G_2-structure on a seven-dimensional Riemannian manifold is equivalent to a spin structure with a Killing spinor. We prove general results about the automorphism group of such structures and we construct new examples. We classify all nearly parallel G_2-manifolds with large symmetry group and in particular all homogeneous nearly parallel G_2-structures.
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Thomas Friedrich, Ines Kath, Andrei Moroianu, Uwe Semmelmann. On nearly parallel G_2-structures. Journal of Geometry and Physics, Elsevier, 1997, 23, pp.259-286. ⟨10.1016/S0393-0440(97)80004-6⟩. ⟨hal-00126037⟩

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