Vol. 316, No. 1, 2022

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

Andrea Loi, Filippo Salis and Fabio Zuddas

Vol. 316 (2022), No. 1, 183–205
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
Authors
Andrea Loi
Dipartimento di Matematica
Università di Cagliari
Cagliari
Italy
Filippo Salis
Dipartimento di Scienze Matematiche
Politecnico di Torino
Torino
Italy
Fabio Zuddas
Dipartimento di Matematica
Università di Cagliari
Cagliari
Italy