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

By Jorge Lauret, Edwin Alejandro Rodríguez Valencia. 2013

54 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0516a09dd422d7a8787b285b5aef91f0c04f6310

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In Applied Mathematics

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In Mathematical Physics

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Citations in the corpus

• Balanced Hermitian structures on almost abelian Lie algebras (2020, methodology): “As shown in [44], the matrix B associated with ade2n |n in this basis is of the form”
• Lattices in almost abelian Lie groups with locally conformal Kähler or symplectic structures (2016, unknown): “This class has appeared recently in several different contexts (see for instance [4, 7, 9, 24, 25]).”