Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
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.
