Kähler–Ricci solitons induced by infinite-dimensional complex space forms

Andrea Loi, Filippo Salis and Fabio Zuddas

Vol. 316 (2022), No. 1, 183–205

DOI: 10.2140/pjm.2022.316.183

Abstract

We exhibit families of nontrivial (i.e., not Kähler–Einstein) radial Kähler–Ricci solitons (KRS), both complete and not complete, which can be Kähler immersed into infinite-dimensional complex space forms. This shows that the triviality of a KRS induced by a finite-dimensional complex space form proved by Loi and Mossa (Proc. Amer. Math. Soc. 149:11 (2020), 4931–4941) does not hold when the ambient space is allowed to be infinite-dimensional. Moreover, we show that the radial potential of a radial KRS induced by a nonelliptic complex space form is necessarily defined at the origin.

Keywords

Kähler metric, Kähler–Ricci solitons, Einstein metrics, Calabi's diastasis function, complex space forms

Mathematical Subject Classification

Primary: 32Q15, 53C55

Milestones

Received: 23 July 2021

Accepted: 27 November 2021

Published: 26 February 2022