Applications of algebraic topology in bounding the rank of the skew-symmetric curvature operator
type: Item
instance of: scholarly article
title: Applications of algebraic topology in bounding the rank of the skew-symmetric curvature operator
zbMATH Open document ID: 1029.53028
DOI: 10.1016/S0166-8641(01)00226-7
author: Tan Zhang
published in: Topology and its Applications
publication date: 2003-03-10T00:00:00Z
review text: Let \(V\) an inner product space of signature \((p,q)\), let \(R\) be an algebraic curvature tensor on \(V\) and let \(R(\cdot)\) be the associated skew-symmetric operator. Assume that the rank of \(R(\cdot)\) is equal to a constant \(r\) on the Grassmannian of nondegenerate 2 planes. Using Stiefel-Whitney classes and \(K\)-theory, the author shows that \(r=2\) if \(p=0\), 1 and \(q\geq 9\) or if \(p=2\) and if \(q\geq 10\) and if \(q\) and \(q+2\) are not powers of 2.
Mathematics Subject Classification ID: 53B20
Mathematics Subject Classification ID: 57R19
zbMATH DE Number: 1879078
zbMATH Keywords: algebraic curvature tensor
zbMATH Keywords: skew-symmetric curvature operator
zbMATH Keywords: Lorentzian and higher signature
zbMATH Keywords: Ivanov-Petrova tensors
reviewed by: Antonio Masiello
MaRDI profile type: Publication
cites work: Vector fields on spheres
cites work: Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts
cites work: Q4943771
cites work: Riemannian manifolds whose skewd-symmetric curvature operator has constant eigenvalues
cites work: Algebraic curvature tensors whose skew-symmetric curvature operator has constant rank 2
cites work: Riemannian manifold in which the skew-symmetric curvature operator has pointwise constant eigenvalues
cites work: Q3685677
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description: scientific article; zbMATH DE number 1879078