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We extend the refined G-structure classification of supersymmetric solutionsof eleven dimensional supergravity. We derive necessary and sufficientconditions for the existence of an arbitrary number of Killing spinors whosecommon isotropy group contains a compact factor acting irreducibly in eightspatial dimensions and which embeds in$(Spin(7)\ltimes\mathbb{R}^8)\times\mathbb{R}$. We use these conditions toexplicitly derive the general local bosonic solution of the Killing spinorequation admitting an N=4 SU(4) structure embedding in a$(Spin(7)\ltimes\mathbb{R}^8)\times\mathbb{R}$ structure, up to aneight-manifold of SU(4) holonomy. Subject to very mild assumptions on the formof the metric, we explicitly derive the general local bosonic solutions of theKilling spinor equation for N=6 Sp(2) structures and N=8 $SU(2)\times SU(2)$structures embedding in a $(Spin(7)\ltimes\mathbb{R}^8)\times\mathbb{R}$structure, again up to eight-manifolds of special holonomy. We constructseveral other classes of explicit solutions, including some for which thepreferred local structure group defined by the Killing spinors does notcorrespond to any holonomy group in eleven dimensions. We also give a detailedgeometrical characterisation of all supersymmetric spacetimes in elevendimensions admitting G-structures with structure groups of the form$(G\ltimes\mathbb{R}^8)\times\mathbb{R}$.Comment: 50 pages, Latex; v2, minor modifications and clarifications;  integrability conditions and typos corrected; v3, 53 pages; changes in  response to referee's comments, additional appendix, typos corrected. Final  version to appear in Phys.Rev.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Eight-manifolds with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>G</mml:mi></mml:math> structure in eleven dimensional supergravity

Eight-manifolds withG structure in eleven dimensional supergravity