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

von Ilias Tergiakidis
Dissertation
Datum der mündl. Prüfung:2017-09-28
Erschienen:2017-12-15
Betreuer:Prof. Dr. Viktor Pidstrygach
Gutachter:Prof. Dr. Viktor Pidstrygach
Gutachter:Prof. Dr. Dorothea Bahns
Zum Verlinken/Zitieren: http://dx.doi.org/10.53846/goediss-6642

 

 

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Zusammenfassung

Englisch

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.
Keywords: Ricci flow; Type I singularities; 4-manifolds
 
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