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Affine curvature homogeneous 3 dimensional Lorentz manifolds
Peter B. Gilkey and Stana NikcevicAbstract
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 members of the family are geodesically complete, others are not. All have vanishing scalar invariants.
- Received:
- 07.06.05
- Published:
- 07.06.05
- MSC Codes:
- 53B20
- Keywords:
- curvature homogeneous, vanishing scalar invariants, lorentz manifold