标题：The nonexistence of rank <mml:math alttext="$4$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>4</mml:mn></mml:math> IP tensors in signature <mml:math alttext="$(1,3)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2002
卷号：31
DOI：10.1155/S0161171202108106
出版社：Hindawi Publishing Corporation
摘要：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.
