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MiS Preprint
96/2006

The global geometry of Riemannian manifolds with commuting curvature operators

Miguel Brozos-Vazquez and Peter B. Gilkey

Abstract

We exhibit manifolds whose Riemann curvature operators commute, i.e. which satisfy the identity R(x,y)R(z,w)=R(z,w)R(x,y) for all x,y,z,w. We work in both the Riemannian and in the higher signature settings. These manifolds have global geometric properties which are quite different in the higher signature setting than in the Riemannian setting. Questions of geodesic completeness and the behaviour of the exponential map are investigated as are other analytic properties.

Received:
07.09.2006
Published:
07.09.2006
MSC Codes:
58B20
Keywords:
algebraic curvature tensor, geodesic completeness, scalar curvature blowup, skew Tsankov manifold

Related publications

inJournal
2007 Repository Open Access
Miguel Brozos-Vazquez and Peter B. Gilkey

The global geometry of Riemannian manifolds with commuting curvature operators

In: Journal of fixed point theory and applications, 1 (2007) 1, pp. 87-96