Steady Ricci Solitons on Complex Line Bundles

Abstract

We show the existence and uniqueness of a one-parameter family of smooth complete $U(1)$-invariant gradient steady Ricci solitons on the total space of any complex line bundle over a Fano Kähler-Einstein base with first Chern class proportional to that of the base. These solitons are non-Kähler except on the total space of the canonical bundle.

arXiv comment35 pages. Comments welcome