G2-structures for N=1 supersymmetric AdS4 solutions of M-theory

Abstract

We study the N=1 supersymmetric solutions of D=11 supergravity obtained as a warped product of four-dimensional anti-de-Sitter space with a seven-dimensional Riemannian manifold M. Using the octonion bundle structure on M we reformulate the Killing spinor equations in terms of sections of the octonion bundle on M. The solutions then define a single complexified G2-structure on M or equivalently two real G2-structures. We then study the torsion of these G2-structures and the relationships between them.