Descripción del título
Bach-flat manifolds a...
Einstein manifolds, being critical for the Hilbert-Einstein functional, are central in Riemannian Geometry and Mathematical Physics. A strategy to construct Einstein metrics consists on deforming a given metric by a conformal factor so that the resulting metric is Einstein. In the present Thesis we follow this approach with special emphasis in dimension four. In this work we classify four-dimensional homogeneous conformally Einstein manifolds and provide a large family of strictly Bach-flat gradient Ricci solitons. We show the existence of Bach-flat structures given as deformations of Riemannian extensions by means of the Cauchy-Kovalevskaya theorem
Monografía
monografia Rebiun32636186 https://catalogo.rebiun.org/rebiun/record/Rebiun32636186 cr#||||||a|a|| 200112s2020 sp o 000 0 eng cd DX1101341044 UMA.RE Gutiérrez Rodríguez, Ixchel Dzohara Bach-flat manifolds and conformally Einstein structures Ixchel Dzohara Gutiérrez Rodríguez 1ª edición Santiago de Compostela Universidade de Santiago de Compostela. Servizo de Publicacións e Intercambio Científico 2020 Santiago de Compostela Santiago de Compostela Universidade de Santiago de Compostela. Servizo de Publicacións e Intercambio Científico Publicaciones del Departamento de Geometría y Topología 142 2020 Unrestricted online access star Einstein manifolds, being critical for the Hilbert-Einstein functional, are central in Riemannian Geometry and Mathematical Physics. A strategy to construct Einstein metrics consists on deforming a given metric by a conformal factor so that the resulting metric is Einstein. In the present Thesis we follow this approach with special emphasis in dimension four. In this work we classify four-dimensional homogeneous conformally Einstein manifolds and provide a large family of strictly Bach-flat gradient Ricci solitons. We show the existence of Bach-flat structures given as deformations of Riemannian extensions by means of the Cauchy-Kovalevskaya theorem Einstein manifolds Estructuras de Einstein Matemáticas Universidad de Santiago de Compostela. Departamento de Geometría y Topología