Geometric Analysis and Topology Seminar

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Steady gradient K\"ahler-Ricci solitons and Calabi-Yau metrics on C^n

Speaker: Charles Cifarelli, Stony Brook University

Location: Warren Weaver Hall 512

Date: Friday, September 29, 2023, 11 a.m.

Synopsis:

 Abstract: I will present a new construction of complete steady gradient K\"ahler-Ricci solitons on C^n, using the theory of hamiltonian 2 forms, introduced by Apostolov-Calderbank-Gauduchon-T{\o}nnesen-Friedman, as an Ansatz. The metrics come in families of two types with distinct geometric behavior, which we call Cao type and Taub-NUT type. In particular, the Cao type and Taub-NUT type families have a volume growth rate of r^n and r^{2n-1}, respectively. Moreover, each Taub-NUT type family contains a codimension 1 subfamily of complete Ricci-flat metrics. This is joint work with V. Apostolov.