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The global geometry of Riemannian manifolds with commuting curvature operators
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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