Vector bundles over Grassmannians and the skew-symmetric curvature operator

Details Vector bundles over Grassmannians and the skew-symmetric curvature operator Vector bundles over Grassmannians and the skew-symmetric curvature operator

2004-07-15

arxiv.org/abs/math/0407284v2

Mathematics

Differential Geometry

This paper has been withdrawn due to a transfer of copyright agreement. The paper will appear in Differential Geometry and its

Scientific paper

A pseudo-Riemannian manifold is said to be spacelike Jordan IP if the Jordan normal form of the skew-symmetric curvature operator depends upon the point of the manifold, but not upon the particular spacelike 2-plane in the tangent bundle at that point. We use methods of algebraic topology to classify connected spacelike Jordan IP pseudo-Riemannian manifolds of signature $(p,q)$, where $q\ge 11$, $p\le \frac{q-6}{4}$ and where the set $\{q, . . ., q+p\}$ does not contain a power of 2.

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