Invariant Solutions of the Yamabe equation on the Koiso-Cao Soliton

Abstract

We consider the non-trivial Ricci soliton on ${\mathbb{CP}}^2\#\overline{{\mathbb{CP}}^2}$ constructed by Koiso and Cao. It is a Kähler metric invariant by the $U(2)$ action on ${\mathbb{CP}}^2\#\overline{{\mathbb{CP}}^2}$. We study its Yamabe equation and prove it has exactly one $U(2)-$invariant solution up to homothecies.

17 pages, 1 figure

References in corpus (1)

• Blow-up phenomena for the Yamabe equation