Rigidity and infinitesimal deformability of Ricci solitons

TL;DR

This paper investigates the rigidity of Ricci solitons, providing an obstruction to their infinitesimal deformations, and demonstrates that even-dimensional complex projective spaces are rigid despite having such deformations.

Contribution

It introduces an obstruction to the integrability of infinitesimal solitonic deformations and applies it to show rigidity of certain complex projective spaces.

Findings

Obstruction to integrability of infinitesimal solitonic deformations.

Even-dimensional complex projective spaces are rigid as Ricci solitons.

Complex projective spaces have infinitesimal deformations but are rigid overall.

Abstract

In this paper, an obstruction against the integrability of certain infinitesimal solitonic deformations is given. Using this obstruction, we show that the complex projective spaces of even complex dimension are rigid as Ricci solitons although they have infinitesimal solitonic deformations.