The nonexistence of rank 4 IP tensors in signature ( 1, 3 )

Kelly Jeanne Pearson and Tan Zhang

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 31, 1-11

Abstract:

Let V be a real vector space of dimension 4 with a nondegenerate symmetric bilinear form of signature ( 1 , 3 ) . We show that there exists no algebraic curvature tensor R on V so that its associated skew-symmetric operator R ( ⋅ ) has rank 4 and constant eigenvalues on the Grassmannian of nondegenerate 2 -planes in V .

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:314571

DOI: 10.1155/S0161171202108106

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