The curvature homogeneity bound for four-dimensional Lorentzian manifolds
نویسندگان
چکیده
We prove that a four-dimensional Lorentzian manifold that is curvature homogeneous of order 3, or CH3 for short, is necessarily locally homogeneous. We also exhibit and classify four-dimensional Lorentzian, CH2 manifolds that are not homogeneous. Our results imply that the Singer index for four-dimensional Lorentzian manifolds is greater or equal to 2. PACS numbers: 04.20, 02.40 AMS classification scheme numbers: 53C50
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