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

A. Loi;F. Salis;F. Zuddas

2022-01-01

---

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.