A non-K\"ahler expanding Ricci soliton with a K\"ahler tangent cone at infinity

TL;DR

This paper constructs a unique non-Kähler expanding Ricci soliton with a Kähler tangent cone at infinity, illustrating a new example of desingularization in geometric analysis.

Contribution

It provides the first example of a non-Kähler AC expanding Ricci soliton with a Kähler tangent cone at infinity, expanding understanding of Ricci soliton structures.

Findings

Existence of a non-Kähler AC expanding Ricci soliton with Kähler tangent cone

Demonstration that certain Kähler cones cannot be smoothed by Kähler-Ricci solitons

New insights into desingularization of Kähler cones

Abstract

We construct an example of an asymptotically conical (AC) non-K\"ahler expanding gradient Ricci soliton that has a K\"ahler tangent cone at infinity. This yields an example of a K\"ahler cone that can be desingularised by a smooth AC expanding gradient Ricci soliton but not by a smooth AC expanding gradient K\"ahler--Ricci soliton.