Explicit Ricci solitons on nilpotent Lie groups - Mathematics > Differential GeometryReport as inadecuate




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



Author: Michael Bradford Williams

Source: https://arxiv.org/







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