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http://dx.doi.org/10.18419/opus-13515
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DC Element | Wert | Sprache |
---|---|---|
dc.contributor.advisor | Semmelmann, Uwe (Prof. Dr.) | - |
dc.contributor.author | Schwahn, Paul | - |
dc.date.accessioned | 2023-09-15T12:46:26Z | - |
dc.date.available | 2023-09-15T12:46:26Z | - |
dc.date.issued | 2023 | de |
dc.identifier.other | 1859709699 | - |
dc.identifier.uri | http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-135348 | de |
dc.identifier.uri | http://elib.uni-stuttgart.de/handle/11682/13534 | - |
dc.identifier.uri | http://dx.doi.org/10.18419/opus-13515 | - |
dc.description.abstract | (1) Stability of Einstein metrics on symmetric spaces of compact type: We prove the linear stability with respect to the Einstein-Hilbert action of the symmetric spaces SU(n), n ≥ 3, and E_6/F_4 . Combined with earlier results, this resolves the stability problem for irreducible symmetric spaces of compact type. | en |
dc.description.abstract | (2) Coindex and rigidity of Einstein metrics on homogeneous Gray manifolds: Any 6-dimensional strict nearly Kähler manifold is Einstein with positive scalar curvature. We compute the coindex of the metric with respect to the Einstein-Hilbert functional on each of the compact homogeneous examples. Moreover, we show that the infinitesimal Einstein deformations on F_1,2 = SU(3)/T_2 are not integrable into a curve of Einstein metrics. | en |
dc.description.abstract | (3) Stability of the Non-Symmetric Space E_7/PSO(8): We prove that the normal metric on the homogeneous space E_7/PSO(8) is stable with respect to the Einstein-Hilbert action, thereby exhibiting the first known example of a non-symmetric metric of positive scalar curvature with this property. | en |
dc.description.abstract | (4) The Lichnerowicz Laplacian on normal homogeneous spaces: We give a new formula for the Lichnerowicz Laplacian on normal homogeneous spaces in terms of Casimir operators. We derive some practical estimates and apply them to the known list of non-symmetric, compact, simply connected homogeneous spaces G/H with G simple whose standard metric is Einstein. This yields many new examples of Einstein metrics which are stable in the Einstein-Hilbert sense, which have long been lacking in the positive scalar curvature setting. | en |
dc.language.iso | en | de |
dc.rights | info:eu-repo/semantics/openAccess | de |
dc.subject.ddc | 510 | de |
dc.title | Stability of Einstein metrics on homogeneous spaces | en |
dc.type | doctoralThesis | de |
ubs.bemerkung.extern | The cumulative part of this thesis consists of four research articles (compare to page 39 of the thesis). | en |
ubs.dateAccepted | 2023-07-07 | - |
ubs.fakultaet | Mathematik und Physik | de |
ubs.institut | Institut für Geometrie und Topologie | de |
ubs.publikation.seiten | xv, 168 | de |
ubs.publikation.typ | Dissertation | de |
ubs.thesis.grantor | Mathematik und Physik | de |
Enthalten in den Sammlungen: | 08 Fakultät Mathematik und Physik |
Dateien zu dieser Ressource:
Datei | Beschreibung | Größe | Format | |
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arbeit.pdf | 1,14 MB | Adobe PDF | Öffnen/Anzeigen |
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