The global geometry of Riemannian manifolds with commuting curvature operators

2006/09/18 by M. Brozos-Vazquez, Brozos-Vazquez, M., P. Gilkey +1
Mathematics · #53C20 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C20

paper · pdf · doi:10.48550/arxiv.math/0609500

arxiv created 2006/09/18 · arxiv updated 2009/12/01

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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