International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 5, Pages 259-269
The nonexistence of rank IP tensors in signature
Department of Mathematics and Statistics, Murray State University, Murray 42071-0009, KY, USA
Received 19 August 2001; Revised 9 February 2002
Copyright © 2002 Kelly Jeanne Pearson and Tan Zhang. 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 be a real vector space of dimension with a nondegenerate symmetric bilinear form of signature . We show that there exists no algebraic curvature tensor on so that its associated skew-symmetric operator has rank and constant eigenvalues on the Grassmannian of nondegenerate -planes in .