Scalar Curvature Rigidity of Warped Product Metrics

We show scalar-mean curvature rigidity of warped products of round spheres of dimension at least 2 over compact intervals equipped with strictly log-concave warping functions. This generalizes earlier results of Cecchini-Zeidler to all dimensions. Moreover, we show scalar curvature rigidity of round...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2024
Hauptverfasser: Bär, Christian, Brendle, Simon, Hanke, Bernhard, Wang, Yipeng
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2024
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/212160
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Scalar Curvature Rigidity of Warped Product Metrics. Christian Bär, Simon Brendle, Bernhard Hanke and Yipeng Wang. SIGMA 20 (2024), 035, 26 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Zusammenfassung:We show scalar-mean curvature rigidity of warped products of round spheres of dimension at least 2 over compact intervals equipped with strictly log-concave warping functions. This generalizes earlier results of Cecchini-Zeidler to all dimensions. Moreover, we show scalar curvature rigidity of round spheres of dimension at least 3 with two antipodal points removed. This resolves a problem in Gromov's ''Four Lectures'' in all dimensions. Our arguments are based on spin geometry.
ISSN:1815-0659