  We derive a complete geometrical characterisation of a large class of
$AdS_3$, $AdS_4$ and $AdS_5$ supersymmetric spacetimes in eleven-dimensional
supergravity using G-structures. These are obtained as special cases of a class
of supersymmetric $\mathbb{R}^{1,1}$, $\mathbb{R}^{1,2}$ and $\mathbb{R}^{1,3}$
geometries, naturally associated to M5-branes wrapping calibrated cycles in
manifolds with $G_2$, SU(3) or SU(2) holonomy. Specifically, the latter class
is defined by requiring that the Killing spinors satisfy the same set of
projection conditions as for wrapped probe branes, and that there is no
electric flux. We show how the R-symmetries of the dual field theories appear
as isometries of the general AdS geometries. We also show how known solutions
previously constructed in gauged supergravity satisfy our more general
G-structure conditions, demonstrate that our conditions for half-BPS $AdS_5$
geometries are precisely those of Lin, Lunin and Maldacena, and construct some
new singular solutions.
