287 research outputs found
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
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