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International Journal of Mathematics and Mathematical Sciences
Volume 31, Issue 5, Pages 259-269

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

Department of Mathematics and Statistics, Murray State University, Murray 42071-0009, KY, USA

Received 19 August 2001; Revised 9 February 2002

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.