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
| Main Authors: | , |
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| Format: | info:eu-repo/semantics/submittedVersion |
| Language: | eng |
| Published: |
2024
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| Online Access: | http://hdl.handle.net/11086/553510 https://doi.org/10.48550/arXiv.1405.6065 |
| _version_ | 1811173598228905984 |
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| author | Lauret, Jorge Rubén Will, Cynthia Eugenia |
| author2 | https://orcid.org/0000-0002-9022-2285 |
| author_facet | https://orcid.org/0000-0002-9022-2285 Lauret, Jorge Rubén Will, Cynthia Eugenia |
| author_sort | Lauret, Jorge Rubén |
| collection | Repositorio Digital Universitario |
| 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 |
| format | info:eu-repo/semantics/submittedVersion |
| id | rdu-unc.553510 |
| institution | Universidad Nacional de Cordoba |
| language | eng |
| publishDate | 2024 |
| record_format | dspace |
| spelling | rdu-unc.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 |
| spellingShingle | Symplectic geometry Curvature flow Lauret, Jorge Rubén Will, Cynthia Eugenia On the symplectic curvature flow for locally homogeneous manifolds |
| title | 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_short | On the symplectic curvature flow for locally homogeneous manifolds |
| title_sort | on the symplectic curvature flow for locally homogeneous manifolds |
| topic | Symplectic geometry Curvature flow |
| 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 |