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scalar curvature rigidity for asymptotically locally hyperbolic manifolds
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-9184-1467
1998 (English)In: Annals of Global Analysis and Geometry, ISSN 0232-704X, E-ISSN 1572-9060, Vol. 16, 1-27 p.Article in journal (Refereed) Published
Abstract [en]

Rigidity results for asymptotically locally hyperbolic manifoldswith lower bounds on scalar curvature are proved using spinor methodsrelated to the Witten proof of the positive mass theorem. The argument isbased on a study of the Dirac operator defined with respect to the Killingconnection. The existence of asymptotic Killing spinors is related to thespin structure on the end. The expression for the mass is calculated andproven to vanish for conformally compact Einstein manifolds with conformalboundary a spherical space form, giving rigidity. In the 4-dimensional case,the signature of the manifold is related to the spin structure on the end andexplicit formulas for the relevant invariants are given.

Place, publisher, year, edition, pages
1998. Vol. 16, 1-27 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-13070OAI: oai:DiVA.org:kth-13070DiVA: diva2:320584
Note
QC 20100525Available from: 2010-05-26 Created: 2010-05-26 Last updated: 2017-12-12Bibliographically approved
In thesis
1. Some applications of dirac operators and eta invariants in geometry
Open this publication in new window or tab >>Some applications of dirac operators and eta invariants in geometry
1999 (English)Doctoral thesis, comprehensive summary (Other scientific)
Place, publisher, year, edition, pages
Stockholm: KTH, 1999. 16 p.
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-2788 (URN)99-2952627-7 (ISBN)
Public defence
1999-05-01, 00:00 (English)
Note
QC 20100525Available from: 2000-01-01 Created: 2000-01-01 Last updated: 2010-05-26Bibliographically approved

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Dahl, Mattias

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