On the symplectic curvature flow for locally homogeneous manifolds

Artículo finalmente publicado en: Lauret, J. y Will, C. (2017). On the symplectic curvature flow for locally homogeneous manifolds. Journal of Symplectic Geometry, 15 (1), 1-49. https://dx.doi.org/10.4310/JSG.2017.v15.n1.a1

Detalles Bibliográficos
Autores principales: Lauret, Jorge Rubén, Will, Cynthia Eugenia
Otros Autores: https://orcid.org/0000-0002-9022-2285
Formato: submittedVersion article
Lenguaje:Inglés
Publicado: 2024
Materias:
Symplectic geometry
Curvature flow
Acceso en línea:http://hdl.handle.net/11086/553510
https://doi.org/10.48550/arXiv.1405.6065
Aporte de:
Repositorio Digital Universitario (UNC) de Universidad Nacional de Córdoba
id I10-R141-11086-553510
record_format dspace
spelling I10-R141-11086-5535102024-09-17T12:12:56Z On the symplectic curvature flow for locally homogeneous manifolds Lauret, Jorge Rubén Will, Cynthia Eugenia https://orcid.org/0000-0002-9022-2285 https://orcid.org/0000-0002-1235-8750 Symplectic geometry Curvature flow Artículo finalmente publicado en: Lauret, J. y Will, C. (2017). On the symplectic curvature flow for locally homogeneous manifolds. Journal of Symplectic Geometry, 15 (1), 1-49. https://dx.doi.org/10.4310/JSG.2017.v15.n1.a1 info:eu-repo/semantics/submittedVersion Fil: Lauret, Jorge Rubén. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina. Fil: Lauret, Jorge Rubén. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Fil: Lauret, Jorge Rubén. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigación y Estudios de Matemática; Argentina. Fil: Will, Cynthia Eugenia. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina. Fil: Will, Cynthia Eugenia. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Fil: Will, Cynthia Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigación y Estudios de Matemática; Argentina. Recently, J. Streets and G. Tian introduced a natural way to evolve an almost-Kähler manifold called the symplectic curvature flow, in which the metric, the symplectic structure and the almost-complex structure are all evolving. We study in this paper different aspects of the flow on locally homogeneous manifolds, including long-time existence, solitons, regularity and convergence. We develop in detail two large classes of Lie groups, which are relatively simple from a structural point of view but yet geometrically rich and exotic: solvable Lie groups with a codimension one abelian normal subgroup and a construction attached to each left symmetric algebra. As an application, we exhibit a soliton structure on most of symplectic surfaces which are Lie groups. A family of ancient solutions which develop a finite time singularity was found; neither their Chern scalar nor their scalar curvature are monotone along the flow and they converge in the pointed sense to a (non-Kähler) shrinking soliton solution on the same Lie group. This research was partially supported by grants from CONICET, FONCYT and SeCyT (Universidad Nacional de Córdoba). info:eu-repo/semantics/submittedVersion Fil: Lauret, Jorge Rubén. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina. Fil: Lauret, Jorge Rubén. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Fil: Lauret, Jorge Rubén. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigación y Estudios de Matemática; Argentina. Fil: Will, Cynthia Eugenia. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina. Fil: Will, Cynthia Eugenia. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Fil: Will, Cynthia Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigación y Estudios de Matemática; Argentina. Matemática Pura 2024-09-05T12:46:53Z 2024-09-05T12:46:53Z 2017 article 1527-5256 http://hdl.handle.net/11086/553510 1540-2347 https://doi.org/10.48550/arXiv.1405.6065 eng De la versión publicada: https://dx.doi.org/10.4310/JSG.2017.v15.n1.a1 Atribución-NoComercial-SinDerivadas 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
institution Universidad Nacional de Córdoba
institution_str I-10
repository_str R-141
collection Repositorio Digital Universitario (UNC)
language Inglés
topic Symplectic geometry
Curvature flow
spellingShingle Symplectic geometry
Curvature flow
Lauret, Jorge Rubén
Will, Cynthia Eugenia
On the symplectic curvature flow for locally homogeneous manifolds
topic_facet Symplectic geometry
Curvature flow
description Artículo finalmente publicado en: Lauret, J. y Will, C. (2017). On the symplectic curvature flow for locally homogeneous manifolds. Journal of Symplectic Geometry, 15 (1), 1-49. https://dx.doi.org/10.4310/JSG.2017.v15.n1.a1
author2 https://orcid.org/0000-0002-9022-2285
author_facet https://orcid.org/0000-0002-9022-2285
Lauret, Jorge Rubén
Will, Cynthia Eugenia
format submittedVersion
article
author Lauret, Jorge Rubén
Will, Cynthia Eugenia
author_sort Lauret, Jorge Rubén
title On the symplectic curvature flow for locally homogeneous manifolds
title_short On the symplectic curvature flow for locally homogeneous manifolds
title_full On the symplectic curvature flow for locally homogeneous manifolds
title_fullStr On the symplectic curvature flow for locally homogeneous manifolds
title_full_unstemmed On the symplectic curvature flow for locally homogeneous manifolds
title_sort on the symplectic curvature flow for locally homogeneous manifolds
publishDate 2024
url http://hdl.handle.net/11086/553510
https://doi.org/10.48550/arXiv.1405.6065
work_keys_str_mv AT lauretjorgeruben onthesymplecticcurvatureflowforlocallyhomogeneousmanifolds
AT willcynthiaeugenia onthesymplecticcurvatureflowforlocallyhomogeneousmanifolds
_version_ 1824552387223748608

Ejemplares similares