EINSTEIN-WEYL DEFORMATIONS AND SUBMANIFOLDS

Motivated by new explicit positive Ricci curvature metrics on the four -sphere which are also Einstein-Weyl, we show that the dimension of th e Einstein-Weyl moduli near certain Einstein metrics is bounded by the rank of the isometry group and that any Weyl manifold can be embedded as a hypersurface with prescribed second fundamental form in some Ein stein-Weyl space. Closed four-dimensional Einstein-Weyl manifolds are proved to be absolute minima of the L(2)-norm of the curvature of Weyl manifolds and a local version of the Lafontaine inequality is obtaine d. The above metrics on the four-sphere are shown to contain minimal h ypersurfaces isometric to S-1 x S-2 whose second fundamental form has constant length.