The global geometry of Riemannian manifolds with commuting curvature operators
Differential Geometry
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0609500,
title = {The global geometry of Riemannian manifolds with commuting curvature operators},
author = {M. Brozos-Vazquez and P. Gilkey},
journal= {arXiv preprint arXiv:math/0609500},
year = {2007}
}