Stability of Einstein Manifolds

This thesis deals with Einstein metrics and the Ricci flow on compact mani- folds. We study the second variation of the Einstein-Hilbert functional on Ein- stein metrics. In the first part of the work, we find curvature conditions which ensure the stability of Einstein manifolds with respect to the Einstein-Hilbert functional, i.e. that the second variation of the Einstein-Hilbert functional at the metric is nonpositive in the direction of transverse-traceless tensors. The second part of the work is devoted to the study of the Ricci flow and how its behaviour close to Einstein metrics is influenced by the variational be- haviour of the Einstein-Hilbert functional. We find conditions which imply that Einstein metrics are dynamically stable or unstable with respect to the Ricci flow and we express these conditions in terms of stability properties of the metric with respect to the Einstein-Hilbert functional and properties of the Laplacian spectrum.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Potsdam

Year

2013

Author dc:creator

• Kröncke, Klaus

Contributors dc:contributor

• Bär, Christian

• Einstein-Mannigfaltigkeiten
• Ricci-Fluss
• Variationsstabilität
• Einstein-Hilbert-Wirkung
• Einstein manifolds
• Ricci flow
• variational stability
• Einstein-Hilbert action

Statement dc:rights

• Creative Commons - Namensnennung, Nicht kommerziell, Keine Bearbeitung 3.0 Deutschland

Repository record source_url

https://publishup.uni-potsdam.de/frontdoor/index/index/docId/6723

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-potsdam:6723