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Stability of Einstein Manifolds

Name: Stability of Einstein Manifolds
Brand: Sudwestdeutscher Verlag Fur Hochschulschriften AG
SKU: 05327763
Price: 56.29 EUR
Availability: InStock
Author: Klaus Kröncke
ISBN: 9783838139081

Klaus Kröncke

Language

English

Book Paperback

Libristo code: 05327763

Publishers Sudwestdeutscher Verlag Fur Hochschulschriften AG, July 2014

This work deals with Einstein metrics and the Ricci flow on compact manifolds. We study the second v... Full description

Libristo code: 05327763

138 b

56.29 € VAT included

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This work deals with Einstein metrics and the Ricci flow on compact manifolds. We study the second variation of the Einstein-Hilbert functional on Einstein 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 behaviour 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.