Henrik Pedersen, Yat Sun Poon, Andrew Swann
Einstein-Weyl Deformations and Submanifolds
The paper is published: Int. J. Math. 7, 5 (1996) 705-719

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)

53C40 Global submanifolds, See also {53B25}

58E11 Critical metrics

Abstract: Motivated by new explicit positive Ricci curvature metrics on the four-sphere
which are also Einstein-Weyl, we show that the dimension of the 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 Einstein-Weyl space.
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 obtained. The above metrics on the four-sphere are
shown to contain minimal hypersurfaces isometric to~$S^1\times S^2$ whose
second fundamental form has constant length.


Keywords: moduli space, Weyl manifold, Einstein-Weyl manifold, minimal hypersurfaces