Three-dimensional Ricci solitons which project to surfaces

Abstract

We study $3$-dimensional Ricci solitons which project via a semi-conformal mapping to a surface. We reformulate the equations in terms of parameters of the map; this enables us to give an ansatz for constructing solitons in terms of data on the surface. A complete description of the soliton structures on all the $3$-dimensional geometries is given, in particular, non-gradient solitons are found on Nil and Sol.

28 pages

Cited by in corpus (2)

• Linear stability of homogeneous Ricci solitons
• On the long-time behavior of type-III Ricci flow solutions