Abstract:
The purpose of this paper is to construct a set of Riemannian metrics on a manifold X with the property that will develop a pinching singularity in finite time when evolved by Ricci flow. More specifically, let , where N n is an arbitrary closed manifold of dimension n≥ 2 which admits an Einstein metric of positive curvature. We construct a (non-empty) set of warped product metrics on the non-compact manifold X such that if , then a smooth solution , t∈[0,T) to the Ricci flow equation exists for some maximal constant T, 0<T<∞, with initial value , and
where K is some compact set .
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 8 March 1999
Rights and permissions
About this article
Cite this article
Simon, M. A class of Riemannian manifolds that pinch when evolved by Ricci flow. manuscripta math. 101, 89–114 (2000). https://doi.org/10.1007/s002290050006
Issue Date:
DOI: https://doi.org/10.1007/s002290050006