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Three-dimensional Einstein-Weyl geometry. (English) Zbl 0778.53041
Several examples of Einstein-Weyl spaces are obtained, discussed and classified. The question of complexification is solved. A simple proof is given that the Einstein-Weyl condition is equivalent to the existence of totally geodesic null hypersurfaces. Some conjectures are presented.

MSC:
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
14M17 Homogeneous spaces and generalizations
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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