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arXiv · 1004.3778

Explicit Ricci solitons on nilpotent Lie groups

Michael Bradford Williams
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Abstract

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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Michael Bradford Williams. 2010-12-01. Explicit Ricci solitons on nilpotent Lie groups. https://arxiv.org/abs/1004.3778

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