scalar curvature rigidity for asymptotically locally hyperbolic manifolds
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
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.
IdentifiersURN: urn:nbn:se:kth:diva-13070OAI: oai:DiVA.org:kth-13070DiVA: diva2:320584
QC 201005252010-05-262010-05-262010-05-26Bibliographically approved