The geometry of weakly-Einstein manifolds

The geometry of Einstein manifiolds is a well studied topic in differential geometry. Einstein metrics appear in the analysis of critical metrics for some Riemannian functionals. They add strong conditions on the manifold, so it is a natural question trying to weaken this condition. This thesis is d...

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Detalles Bibliográficos
Autor: Mariño Villar, Rodrigo
Tipo de recurso: tesis doctoral
Fecha de publicación:2021
País:España
Institución:Universidad de Santiago de Compostela (USC)
Repositorio:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
Idioma:inglés
OAI Identifier:oai:minerva.usc.gal:10347/26603
Acceso en línea:http://hdl.handle.net/10347/26603
Access Level:acceso abierto
Palabra clave:Materias::Investigación::12 Matemáticas::1204 Geometría::120404 Geometría diferencial
Materias::Investigación::12 Matemáticas::1204 Geometría::120411 Geometría de Riemann
Materias::Investigación::12 Matemáticas::1201 Algebra::120109 Algebra de Lie
Descripción
Sumario:The geometry of Einstein manifiolds is a well studied topic in differential geometry. Einstein metrics appear in the analysis of critical metrics for some Riemannian functionals. They add strong conditions on the manifold, so it is a natural question trying to weaken this condition. This thesis is devoted to the study of the so called weakly-Einstein manifolds. This conditions are analyzed under some special assumptions in different frames such as locally conformally flat manifolds, hypersurfaces or homogeneous manifolds. Moreover, other conditions related with the weakly-Einstein ones are also studied which are the generalized Einstein one and the two-loop renormalization flow.