Affine curvature homogeneous 3 dimensional Lorentz manifolds

Peter B. Gilkey and Stana Nikcevic

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Submission date: 07. Jun. 2005
Pages: 12
published in: International journal of geometric methods in modern physics, 2 (2005) 5, p. 737-749 
DOI number (of the published article): 10.1142/S0219887805000776
Bibtex
MSC-Numbers: 53B20
Keywords and phrases: curvature homogeneous, vanishing scalar invariants, lorentz manifold
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Abstract:
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.