2025/02/12 by James Isenberg, Isenberg, James, Dan Knopf +5
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research
paper · pdf · doi:10.48550/arxiv.2502.08500
We demonstrate that any four-dimensional shrinking Ricci soliton (\mathcal B × \mathbb S2, g), where \mathcal B is any two-dimensional complete noncompact surface and g is a warped product metric over the base \mathcal B, has to be isometric to the generalized cylinder \mathbb R2×\mathbb S2 equipped with the standard cylindrical metric. After completing this classification, we study Ricci flow solutions that are multiply warped products -- but not products -- and provide rigorous examples of the formation of generalized cylinder singularity models \mathbb Rk×\mathbb S^ℓ.