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dc.contributor.author
Arroyo, Romina Melisa
dc.date.available
2015-10-01T19:02:44Z
dc.date.issued
2013-08
dc.identifier.citation
Arroyo, Romina Melisa; The Ricci flow in a class of solvmanifolds; Elsevier; Differential Geometry and its Applications; 31; 4; 8-2013; 472-485
dc.identifier.issn
0926-2245
dc.identifier.uri
http://hdl.handle.net/11336/2271
dc.description.abstract
In this paper, we study the Ricci flow of solvmanifolds whose Lie algebra has an abelian ideal of codimension one, by using the bracket flow. We prove that solutions to the Ricci flow are immortal, the omega-limit of bracket flow solutions is a single point, and that for any sequence of times there exists a subsequence in which the Ricci flow converges, in the pointed topology, to a manifold which is locally isometric to a flat manifold. We give a functional which is non-increasing along a normalized bracket flow that will allow us to prove that given a sequence of times, one can extract a subsequence converging to an algebraic soliton, and to determine which of these limits are flat. Finally, we use these results to prove that if a Lie group in this class admits a Riemannian metric of negative sectional curvature, then the curvature of any Ricci flow solution will become negative in finite time.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Elsevier
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.subject
Ricci Flow
dc.subject
Solvmanifolds
dc.subject
Bracket Flow
dc.subject
Negative Curvature
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
The Ricci flow in a class of solvmanifolds
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2016-03-30 10:35:44.97925-03
dc.journal.volume
31
dc.journal.number
4
dc.journal.pagination
472-485
dc.journal.pais
Países Bajos
dc.journal.ciudad
Amsterdam
dc.description.fil
Fil: Arroyo, Romina Melisa. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
dc.journal.title
Differential Geometry and its Applications
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0926224513000296
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1016/j.difgeo.2013.04.002
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