A note on Hang-Wang’s hemisphere rigidity theorem

Let ( M , g ) be a compact manifold with boundary and R i c g ≥ ( n - 1 ) g , Hang and Wang proved that ( M , g ) is isometric to the standard hemisphere if ∂ M is convex and isometric to S n - 1 ( 1 ) . We prove some rigidity theorems when ∂ M is isometric to a product manifold where one factor i...

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Veröffentlicht in:	Mathematische Zeitschrift 2020-12, Vol.296 (3-4), p.901-909
1. Verfasser:	Lai, Mijia
Format:	Artikel
Sprache:	eng
Schlagworte:	Manifolds Mathematics Mathematics and Statistics Rigidity Theorems
Online-Zugang:	Volltext
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Zusammenfassung:	Let ( M , g ) be a compact manifold with boundary and R i c g ≥ ( n - 1 ) g , Hang and Wang proved that ( M , g ) is isometric to the standard hemisphere if ∂ M is convex and isometric to S n - 1 ( 1 ) . We prove some rigidity theorems when ∂ M is isometric to a product manifold where one factor is the standard sphere.
ISSN:	0025-5874 1432-1823
DOI:	10.1007/s00209-020-02469-w