Vector bundles over Grassmannians and the skew-symmetric curvature operator

2004/07/15 by Iva Stavrov, Stavrov, Iva
Mathematics · #53B30 #55R99 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #math.AT #math.DG #msc:53B30 #msc:55R99

paper · pdf · doi:10.48550/arxiv.math/0407284

This paper has been withdrawn due to a transfer of copyright agreement.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

arxiv created 2005/05/28 · arxiv updated 2009/12/01

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≥ 11, p≤ (q-6)/(4) and where the set \q, . . ., q+p\ does not contain a power of 2.

Related

• Algebraic curvature tensors for indefinite metrics whose skew-symmetric curvature operator has constant Jordan normal form
• Manifolds which are Ivanov-Petrova or k-Stanilov
• Nilpotent Spacelike Jorden Osserman pseudo-Riemannian manifolds
• Szabo Osserman IP Pseudo-Riemannian manifolds
• Riemannian manifolds of dimension 7 whose skew-symmetric curvature operator has constant eigenvalues