时间：2025年10月27日（星期一）20:00-21:00
Zoom ID: 995 0538 3016
Passcode: 251027
主讲人：Andrea Loi, University of Cagliari
讲座主题：Holomorphic Isometries from cscK Manifolds into Complex Space Forms
讲座摘要：We survey holomorphic isometries from Kähler manifolds with constant scalar curvature (cscK) into the three complex space forms, complex hyperbolic, flat, and projective, allowing both finite- and infinite-dimensional targets. The talk is organized around three themes: (i) complex space forms (Calabi’s rigidity/extension and explicit models); (ii) homogeneous Kähler manifolds (structure results and projective realizations via Rawnsley’s map); and (iii) Kähler–Einstein (KE) manifolds (codimension bounds and positivity/vanishing phenomena for the scalar curvature). While the cases of complex space forms and homogeneous Kähler manifolds admit a complete classification, the KE setting still features many open conjectures, which will be outlined. We then turn to general cscK metrics and, in the radial setting, obtain a complete classification of non-negative projectively induced cscK metrics: besides the Fubini–Study family (scal > 0), the only scalar-flat examples are the flat metric and the Burns–Simanca metric.
Joint work with C. Arezzo, R. Mossa, G. Placini, M. Zedda, and F. Zuddas.
