On nearly parallel G_2-structures

Thomas Friedrich (1) , Ines Kath (1) , Andrei Moroianu (2) , Uwe Semmelmann (1)

1 HUB - Institut für Reine Mathematik
2 CMLS - Centre de Mathématiques Laurent Schwartz

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.

Mots clés: G2-structures; Sasakian manifolds; Killing spinors

Domaines: Géométrie différentielle [math.DG]

Thomas Friedrich, Ines Kath, Andrei Moroianu, Uwe Semmelmann. On nearly parallel G_2-structures. Journal of Geometry and Physics, 1997, 23, pp.259-286. ⟨10.1016/S0393-0440(97)80004-6⟩. ⟨hal-00126037⟩