Curvature Blow-up in Doubly-warped Product Metrics Evolving by Ricci Flow

For any manifold Np admitting an Einstein metric with positive Einstein constant, we study the behavior of the Ricci flow on high-dimensional products M = Np × Sq+1 with doubly warped product metrics. In particular, we provide a rigorous construction of local, type II, conical singularity formation on such spaces. It is shown that for any k > 1 there exists a solution with curvature blow-up rateRm ∞ (t) (T ? t)?k with singularity modeled on a Ricci-flat cone at parabolic scales.