Curvature blow-up in doubly-warped product metrics evolving by Ricci flow

For any manifold N[superscript p] admitting an Einstein metric with positive Einstein constant, we study the behavior of the Ricci flow on high-dimensional products M = N[superscript p] X S[superscript q+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 rate [double vertical bar]Rm[double vertical bar]infinity symbol [is greater than or approximately equal to] (T – t)[superscript – k] with singularity modeled on a Ricci-flat cone at parabolic scales