Three-dimensional Ricci solitons which project to surfaces

Details Three-dimensional Ricci solitons which project to surfaces Three-dimensional Ricci solitons which project to surfaces

2005-10-14

arxiv.org/abs/math/0510313v1

Mathematics

Differential Geometry

28 pages

Scientific paper

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.

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