Explicit Ricci solitons on nilpotent Lie groups

Details Explicit Ricci solitons on nilpotent Lie groups Explicit Ricci solitons on nilpotent Lie groups

2010-04-21

arxiv.org/abs/1004.3778v2

Mathematics

Differential Geometry

24 pages, no figures; typos corrected and exposition streamlined

Scientific paper

We consider Ricci flow on two classes of nilpotent Lie groups that generalize the three-dimensional Heisenberg group: the higher-dimensional classical Heisenberg groups, and the groups of real unitriangular matrices. Each group is known to admit a Ricci soliton, but we construct them \textit{explicitly} on each group. In the first case, this is done using Lott's blowdown method, whereby we demonstrate convergence of arbitrary diagonal metrics to the solitons. In the second case, which is more complicated, we obtain the solitons using a suitable ansatz.

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