# Local invariants of four-dimensional Riemannian manifolds and their application to the Ricci flow

 dc.contributor.advisor Pidstrygach, Viktor Prof. Dr. dc.contributor.author Tergiakidis, Ilias dc.date.accessioned 2017-12-15T09:10:22Z dc.date.available 2017-12-15T09:10:22Z dc.date.issued 2017-12-15 dc.identifier.uri http://hdl.handle.net/11858/00-1735-0000-0023-3FB1-8 dc.identifier.uri http://dx.doi.org/10.53846/goediss-6642 dc.language.iso eng de dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/ dc.subject.ddc 510 de dc.title Local invariants of four-dimensional Riemannian manifolds and their application to the Ricci flow de dc.type doctoralThesis de dc.contributor.referee Pidstrygach, Viktor Prof. Dr. dc.date.examination 2017-09-28 dc.description.abstracteng In this thesis, we study the four-dimensional Ricci flow with the help of local invariants.If $(M^4, g(t))$ is a solution to the Ricci flow and $x \in M$, we can associate to the point $x$ a one-parameter family of curves, which lie on a smooth quadric in $\mathbb{P}(T_x M \otimes \mathbb{C})$. This allows us to reformulate the Cheeger-Gromov-Hamilton Compactness Theorem in the context of these curves. Furthermore we study Type I singularities in dimension four and give a characterization of the corresponding singularity models in the context of these curves as well. de dc.contributor.coReferee Bahns, Dorothea Prof. Dr. dc.subject.eng Ricci flow de dc.subject.eng Type I singularities de dc.subject.eng 4-manifolds de dc.identifier.urn urn:nbn:de:gbv:7-11858/00-1735-0000-0023-3FB1-8-6 dc.affiliation.institute Fakultät für Mathematik und Informatik de dc.subject.gokfull Mathematics (PPN61756535X) de dc.identifier.ppn 1009206885
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