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

Abstract

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