Vector bundles over Grassmannians and the skew-symmetric curvature operator

• Published in: Differential geometry and its applications Vol. 23; no. 2; pp. 128 - 148
• Main Author: Stavrov, Iva
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-09-2005
• Subjects: Skew-symmetric curvature operator; Spacelike Jordan IP manifolds; SW-filtration; Symmetric vector bundles; Vector bundles over Grassmannians; secondary; Vector bundles over Grassmannians; Symmetric vector bundles; Spacelike Jordan IP manifolds; Skew-symmetric curvature operator; SW-filtration; primary
• ISSN: 0926-2245; 1872-6984
• DOI: 10.1016/j.difgeo.2005.05.006

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
⩾
11
,
p
⩽
q
−
6
4
and where the set
{
q
,
…
,
q
+
p
}
does not contain a power of 2.