García Río, EduardoVázquez Abal, María ElenaMariño Villar, Rodrigo2021-07-262021-07-262021http://hdl.handle.net/10347/26603The 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.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Riemannian geometryEinstein ManifoldsHomogeneous manifoldsHypersurfacesTwo-loopMaterias::Investigación::12 Matemáticas::1204 Geometría::120404 Geometría diferencialMaterias::Investigación::12 Matemáticas::1204 Geometría::120411 Geometría de RiemannMaterias::Investigación::12 Matemáticas::1201 Algebra::120109 Algebra de Liedoctoral thesisopen access