Englert-type solutions of d=11 supergravity [PDF]
E. K. LoginovA family of geometries on S^7 arise as solutions of the classical equations of motion in 11 dimensions. In addition to the conventional riemannian geometry and the two exceptional Cartan-Schouten compact flat geometries with torsion, one can also obtain non-flat geometries with torsion. This torsion is given locally by the structure constants of a nonassociative geodesic loop in the affinely connected space.View original: http://arxiv.org/abs/1307.0097
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