Kaehler Ricci solitons induced by infinite dimensional complex space forms

TL;DR

This paper constructs non-trivial radial Kaehler-Ricci solitons that can be immersed into infinite dimensional complex space forms, revealing new phenomena not seen in finite dimensions.

Contribution

It demonstrates the existence of non-trivial radial KRS immersed in infinite dimensional complex space forms, extending previous finite-dimensional results.

Findings

Existence of non-trivial radial KRS in infinite dimensions

Radial potential of KRS in non-elliptic forms is defined at the origin

Infinite dimensional setting allows for non-trivial KRS beyond finite-dimensional limitations

Abstract

We exhibit families of non trivial (i.e. not Kaehler-Einstein) radial Kaehler-Ricci solitons (KRS), both complete and not complete, which can be Kaehler immersed into infinite dimensional complex space forms. This result shows that the triviality of a KRS induced by a finite dimensional complex space form proved in [12] 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 non-elliptic complex space form is necessarily defined at the origin.