1212.5908 (Alfonso García-Parrado Gómez-Lobo)

On the characterization of non-degenerate foliations of
pseudo-Riemannian manifolds with conformally flat leaves    [PDF]

Alfonso García-Parrado Gómez-Lobo

A necessary and sufficient condition for the leaves of a {\em non-degenerate} foliation of a pseudo-Riemannian manifold to be conformally flat is developed. The condition mimics the classical condition of the vanishing of the Weyl or Cotton tensor establishing the conformal flatness of a pseudo-Riemannian manifold in the sense that it is also formulated in terms of the vanishing of certain tensors. These tensors play the role of the Weyl or the Cotton tensors and they are defined in terms of the distribution generating the leaves of the foliation and the curvature of a linear torsion-free connection (the {\em bi-conformal connection}) which is also defined from the same distribution.

View original: http://arxiv.org/abs/1212.5908