Artículos de revistas
On the Chern-Ricci flow and its solitons for Lie groups
Fecha
2015-09Registro en:
Lauret, Jorge Ruben; Rodriguez Valencia, Edwin Alejandro; On the Chern-Ricci flow and its solitons for Lie groups; Wiley VCH Verlag; Mathematische Nachrichten; 288; 13; 9-2015; 1512-1526
0025-584X
CONICET Digital
CONICET
Autor
Lauret, Jorge Ruben
Rodriguez Valencia, Edwin Alejandro
Resumen
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.