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The global geometry of Riemannian manifolds with commuting curvature operators

M. Brozos-Vazquez·P. Gilkey
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Abstract

We give manifolds in both the Riemannian and in the higher signature settings whose Riemann curvature operators commute, i.e. which satisfy R(a,b)R(c,d)=R(c,d)R(a,b) for all tangent vectors. These manifolds have global geometric phenomena which are quite different for higher signature manifolds than they are for Riemannian manifolds. Our focus is on global properties; questions of geodesic completeness and the behaviour of the exponential map are investigated.

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M. Brozos-Vazquez, P. Gilkey. 2006-09-18. The global geometry of Riemannian manifolds with commuting curvature operators. https://arxiv.org/abs/math/0609500

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