Three-dimensional Einstein-Weyl geometry. (English) Zbl 0778.53041

Pedersen, H.; Tod, K. P.

Adv. Math. 97, No. 1, 74-109 (1993).

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.

Reviewer: A.Szybiak (Waterloo)

MSC:

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

Keywords:

minitwistor space; complex space; signature; geodesics; Einstein-Weyl space; Killing field; twistor; analytic