Finite-Time Singularities of the Kähler--Ricci Flow on a $\mathbb{C}P^m$-Bundle over a Product of Kähler--Einstein Manifolds

RESUMO

In this paper, we study the Kähler--Ricci flow on $\mathbb{C}P^m$-bundles over a product of Kähler--Einstein manifolds, starting from an initial metric with Calabi symmetry. We prove that every finite-time singularity arising along the flow must be of Type~I.