Quotient space solutions of 11-dimensional supergravity (Q1071335)

All the Freund-Rubin type solutions of the 11-dimensional supergravity with a simply connected quotient space G/H as the compact 7-dimensional manifold are found. Their geometries depend only on the imbedding of \(H\subset G\) and the Riemannian structure of G/H. In particular \[ SU_ 3\times SU_ 2\times U_ 1/SU_ 2\times U_ 1\times U_ 1 \] Einstein solutions are discussed in detail.