Vector bundles over Grassmannians and the skew-symmetric curvature operator

Iva Stavrov

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arXiv · math/0407284

Vector bundles over Grassmannians and the skew-symmetric curvature operator

Iva Stavrov

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Abstract

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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Iva Stavrov. 2005-05-28. Vector bundles over Grassmannians and the skew-symmetric curvature operator. https://arxiv.org/abs/math/0407284

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