Impossible Einstein-Weyl geometries. (English) Zbl 0984.53019

Slovák, Jan (ed.) et al., The proceedings of the 19th Winter School “Geometry and physics”, Srní, Czech Republic, January 9-15, 1999. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 63, 17-22 (2000).
In the joint paper of the author with K. P. Tod [J. Reine Angew. Math. 491, 183-198 (1997; Zbl 0876.53029)] they showed all local solutions of the Einstein-Weyl equations in three dimensions, where the background metric is homogeneous with unimodular isometry group. In particular, they proved that there are no solutions with Nil or Sol as background metric. In this note, these two special cases are presented.
For the entire collection see [Zbl 0940.00040].


53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C30 Differential geometry of homogeneous manifolds


Zbl 0876.53029