In this paper, we study the construction of α-conformally equivalent statistical manifolds for a given symmetric cubic form on a Riemannian manifold. In particular, we describe a method to obtain α-conformally equivalent connections from the relation between tensors and the symmetric cubic form.

We show which Thurston-geometries in dimensions 3 and 4 admit invariant conformally flat or half-conformally flat metrics. 1. Threeand four-dimensional geometries A geometry in the sense of Thurston is a pair (X, G) where X is a simply connected smooth manifold on which the connected Lie group G acts smoothly in a transitive fashion such that the following hold: (1) the stabilizer of a point is...

This paper describes the connection between scattering matrices on conformally compact asymptotically Einstein manifolds and conformally invariant objects on their boundaries at infinity. This connection is a manifestation of the general principle that the far field phenomena on a conformally compact Einstein manifold are related to conformal theories on its boundary at infinity. This relations...

1. Statement of the results This paper describes the connection between scattering matrices on conformally compact asymptotically Einstein manifolds and conformally invariant objects on their boundaries at infinity. This connection is a manifestation of the general principle that the far field phenomena on a conformally compact Einstein manifold are related to conformal theories on its boundary...