Using canonical forms on S^7, viewed as an SU(2) bundle over S^4, we
introduce consistent ansatze for the 4-form field strength of
eleven-dimensional supergravity and rederive the known squashed, stretched, and
the Englert solutions. Further, by rewriting the metric of S^7 as a U(1) bundle
over CP^3, we present yet more general ansatze. As a result, we find a new
compactifying solution of the type AdS_5\times CP^3, where CP^3 is stretched
along its S^2 fiber. We also find a new solution of AdS_2\times H^2\times S^7
type in Euclidean space.Comment: 15 pages, revised sec. 4, included new CP^3 and S^7
compactifications, published versio