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arXiv · 1311.0832

On the Chern-Ricci flow and its solitons for Lie groups

Jorge Lauret·Edwin Alejandro Rodriguez Valencia
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Abstract

This paper is concerned with Chern-Ricci flow evolution of left-invariant hermitian structures on Lie groups. We study the behavior of a solution, as t is approaching the first time singularity, by rescaling in order to prevent collapsing and obtain convergence in the pointed (or Cheeger-Gromov) sense to a Chern-Ricci soliton. We give some results on the Chern-Ricci form and the Lie group structure of the pointed limit in terms of the starting hermitian metric and, as an application, we obtain a complete picture for the class of solvable Lie groups having a codimension one normal abelian subgroup. We have also found a Chern-Ricci soliton hermitian metric on most of the complex surfaces which are solvmanifolds, including an unexpected shrinking soliton example.

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Jorge Lauret, Edwin Alejandro Rodriguez Valencia. 2013-11-04. On the Chern-Ricci flow and its solitons for Lie groups. https://arxiv.org/abs/1311.0832

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