2024/10/31 by Charles Cifarelli, Cifarelli, Charles · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2410.23645
openalex publication_date 2024/10/31 · openalex created_date 2024/11/14 · openalex updated_date 2026/07/28
Let B be a Kähler-Einstein Fano manifold, and L → B be a suitable root of the canonical bundle. We give a construction of complete Calabi-Yau metrics and gradient shrinking, steady, and expanding Kähler-Ricci solitons on the total space M, \rm dimℂ M = n of certain vector bundles E → B, composed of direct sums of powers of L. We employ the theory of hamiltonian 2-forms [2, 3] as an Ansatz, thus generalizing recent work of the author and Apostolov on ℂn [5], as well as that of Cao, Koiso, Feldman-Ilmanen-Knopf, Futaki-Wang, and Chi Li [10, 26, 23, 24, 30] when E has Calabi symmetry. As a result, we obtain new examples of asymptotically conical Kähler shrinkers, Calabi-Yau metrics with ALF-like volume growth, and steady solitons with volume growth R(4n-2)/(3).