S1 x S2 as a bag membrane and its Einstein-Weyl geometry

In the hybrid skyrmion in which an anti-de Sitter bag is embedded into the skyrmion configuration a S1 x S2 membrane is lying on the compactified spatial infinity of the bag. The connection between the quark degrees of freedom and the mesonic ones is made through the membrane. This 3-dimensional manifold is at the same time Weyl-Einstein space. We present what is known until the present time to people working in the differential geometry of these spaces. (author). 11 refs