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dc.contributor.author
Lafuente, Ramiro Augusto
dc.contributor.author
Lauret, Jorge Ruben
dc.date.available
2016-11-30T15:50:35Z
dc.date.issued
2014-10
dc.identifier.citation
Lafuente, Ramiro Augusto; Lauret, Jorge Ruben; Structure of homogeneous Ricci solitons and the Alekseevskii conjecture; International Press Boston; Journal of Differential Geometry; 98; 2; 10-2014; 315-347
dc.identifier.issn
0022-040X
dc.identifier.uri
http://hdl.handle.net/11336/8500
dc.description.abstract
We bring new insights into the longstanding Alekseevskii conjecture, namely that any connected homogeneous Einstein manifold of negative scalar curvature is diffeomorphic to a Euclidean space, by proving structural results which are actually valid for any homogeneous expanding Ricci soliton, and generalize many well-known results on Einstein solvmanifolds, solvsolitons, and nilsolitons. We obtain that any homogeneous expanding Ricci soliton M=G/KM=G/K is diffeomorphic to a product U/K×NU/K×N, where UU is a maximal reductive Lie subgroup of GG and NN is the maximal nilpotent normal subgroup of GG, such that the metric restricted to NN is a nilsoliton. Moreover, strong compatibility conditions between the metric and the action of UU on NN by conjugation must hold, including a nice formula for the Ricci operator of the metric restricted to U/KU/K. Our main tools come from geometric invariant theory. As an application, we give many Lie theoretical characterizations of algebraic solitons, as well as a proof of the fact that the following a priori much stronger result is actually equivalent to Alekseevskii’s conjecture: Any expanding algebraic soliton is diffeomorphic to a Euclidean space.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
International Press Boston
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Ricci Solitons
dc.subject
Homogeneous Manifolds
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Alekseevskii Conjecture
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Matemática Pura
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Matemáticas
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CIENCIAS NATURALES Y EXACTAS
dc.title
Structure of homogeneous Ricci solitons and the Alekseevskii conjecture
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2016-11-25T14:01:54Z
dc.journal.volume
98
dc.journal.number
2
dc.journal.pagination
315-347
dc.journal.pais
Estados Unidos
dc.description.fil
Fil: Lafuente, Ramiro Augusto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina. Universidad Nacional de Córdoba; Argentina
dc.description.fil
Fil: Lauret, Jorge Ruben. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina. Universidad Nacional de Córdoba; Argentina
dc.journal.title
Journal of Differential Geometry
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://projecteuclid.org/euclid.jdg/1406552252
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1212.6511v2
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