Affine curvature homogeneous 3-dimensional Lorentz Manifolds

We study a family of 3-dimensional Lorentz manifolds. Some members of the family are 0-curvature homogeneous, 1-affine curvature homogeneous, but not 1-curvature homogeneous. Some are 1-curvature homogeneous but not 2-curvature homogeneous. All are 0-modeled on indecomposible local symmetric spaces. Some of the members of the family are geodesically complete, others are not. All have vanishing scalar invariants

Isometry groups of k-curvature homogeneous pseudo-Riemannian manifolds

We study the isometry groups and Killing vector fields of a family of pseudo-Riemannian metrics on Euclidean space which have neutral signature (3+2p,3+2p). All are p+2 curvature homogeneous, all have vanishing Weyl scalar invariants, all are geodesically complete, and all are 0-curvature modeled on an indecomposible symmetric space. Some of these manifolds are not p+3 curvature homogeneous. Some are homogeneous but not symmetric