New compactifications of 11-dimensional supergravity

Using canonical forms on S7, viewed as an SU(2) bundle over S4, we introduce consistent ansätze for the 4-form field strength of 11-dimensional supergravity and rederive the known squashed, stretched and the Englert solutions. Furthermore, by rewriting the metric of S7 as a U(1) bundle over CP3, we present yet more general ansätze. As a result, we find a new compactifying solution of the type AdS5 × CP3, where CP3 is stretched along its S2 fiber. We also find a new solution of AdS2 × H2 × S7 type in Euclidean space. (paper)