RT Dissertation/Thesis
T1 Bach-flat manifolds and conformally Einstein structures
A1 Gutiérrez Rodríguez, Ixchel Dzohara
K1 Bach tensor
K1 Conformally Einstein manifolds
K1 Ricci solitons
AB 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. This is the first non-trivial case where the conformally Einstein condition is not tensorial and there are topological obstructions to the existence of Einstein metrics. The conformally Einstein condition is given by a overdetermined PDE-system. Hence the consideration of necessary conditions to be conformally Einstein are of special relevance: the Bach-flat condition is central. In this Thesis 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.
YR 2019
FD 2019
LK http://hdl.handle.net/10347/19468
UL http://hdl.handle.net/10347/19468
LA eng
DS Minerva
RD 6 jun 2026