Three-dimensional Ricci solitons which project to surfaces

Paul Baird; Laurent Danielo

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Three-dimensional Ricci solitons which project to surfaces

Paul Baird·Laurent Danielo

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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.

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BibTeX RIS

Paul Baird, Laurent Danielo. 2005-10-14. Three-dimensional Ricci solitons which project to surfaces. https://arxiv.org/abs/math/0510313

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