International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 5, Pages 259-269
doi:10.1155/S0161171202108106

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

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.