Canad. Math. Bull. 53(2010), 412-424
Printed: Sep 2010
We completely classify three-dimensional Lorentz manifolds, curvature homogeneous up to order one, equipped with Einstein-like metrics. New examples arise with respect to both homogeneous examples and three-dimensional Lorentz manifolds admitting a degenerate parallel null line field.
Lorentz manifolds, curvature homogeneity, Einstein-like metrics
53C50 - Lorentz manifolds, manifolds with indefinite metrics
53C20 - Global Riemannian geometry, including pinching [See also 31C12, 58B20]
53C30 - Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]