Curvature flows for almost-hermitian Lie groups

We study curvature flows in the locally homogeneous case (e.g. compact quotients of Lie groups, solvmanifolds, nilmanifolds) in a unified way, by considering a generic flow under just a few natural conditions on the broad class of almost-hermitian structures. As a main tool, we use an ODE system def...

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Autor principal: Lauret, Jorge Rubén
Formato: article
Lenguaje:Inglés
Publicado: 2022
Materias:
Curvature
Flow
Almost-Hermitian
Lie groups
Acceso en línea:http://hdl.handle.net/11086/29975
https://doi.org/10.48550/arXiv.1306.5931
Aporte de:
Repositorio Digital Universitario (UNC) de Universidad Nacional de Córdoba
id I10-R141-11086-29975
record_format dspace
institution Universidad Nacional de Córdoba
institution_str I-10
repository_str R-141
collection Repositorio Digital Universitario (UNC)
language Inglés
topic Curvature
Flow
Almost-Hermitian
Lie groups
spellingShingle Curvature
Flow
Almost-Hermitian
Lie groups
Lauret, Jorge Rubén
Curvature flows for almost-hermitian Lie groups
topic_facet Curvature
Flow
Almost-Hermitian
Lie groups
description We study curvature flows in the locally homogeneous case (e.g. compact quotients of Lie groups, solvmanifolds, nilmanifolds) in a unified way, by considering a generic flow under just a few natural conditions on the broad class of almost-hermitian structures. As a main tool, we use an ODE system defined on the variety of 2n-dimensional Lie algebras, called the bracket flow, whose solutions differ from those to the original curvature flow by only pull-back by time-dependent diffeomorphisms. The approach, which has already been used to study the Ricci flow on homogeneous manifolds, is useful to better visualize the possible pointed limits of solutions, under diverse rescalings, as well as to address regularity issues. Immortal, ancient and self-similar solutions arise naturally from the qualitative analysis of the bracket flow. The Chern-Ricci flow and the symplectic curvature flow are considered in more detail.
format article
author Lauret, Jorge Rubén
author_facet Lauret, Jorge Rubén
author_sort Lauret, Jorge Rubén
title Curvature flows for almost-hermitian Lie groups
title_short Curvature flows for almost-hermitian Lie groups
title_full Curvature flows for almost-hermitian Lie groups
title_fullStr Curvature flows for almost-hermitian Lie groups
title_full_unstemmed Curvature flows for almost-hermitian Lie groups
title_sort curvature flows for almost-hermitian lie groups
publishDate 2022
url http://hdl.handle.net/11086/29975
https://doi.org/10.48550/arXiv.1306.5931
work_keys_str_mv AT lauretjorgeruben curvatureflowsforalmosthermitianliegroups
bdutipo_str Repositorios
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