The global geometry of Riemannian manifolds with commuting curvature operators

Details The global geometry of Riemannian manifolds with commuting curvature operators The global geometry of Riemannian manifolds with commuting curvature operators

2006-09-18

arxiv.org/abs/math/0609500v1

Mathematics

Differential Geometry

Scientific paper

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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