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- W2008199944 abstract "Let ( M n , g ) , n ⩾ 3 , be a smooth closed Riemannian manifold with positive scalar curvature R g . There exists a positive constant C = C ( M , g ) , which is a geometric invariant, such that R g ⩽ n ( n − 1 ) C . In this paper we prove that R g = n ( n − 1 ) C if and only if ( M n , g ) is isometric to the Euclidean sphere S n ( C ) with constant sectional curvature C . Also, there exists a Riemannian metric g on M n such that the scalar curvature satisfies the pinched condition, n 2 ( n − 2 ) n − 1 C < R g ⩽ n ( n − 1 ) C , if and only if M n is diffeomorphic to the standard sphere S n . Soit ( M n , g ) , n ⩾ 3 , une variété riemannienne compacte C ∞ de courbure scalaire R g positive. Il existe une constante positive C = C ( M , g ) , qui est un invariant géométrique, telle que R g ⩽ n ( n − 1 ) C . Dans cet article, on démontre que R g = n ( n − 1 ) C si et seulement si ( M n , g ) est isométrique à la sphère euclidienne S n ( C ) à courbure sectionnelle C constante. De plus, il existe une métrique riemannienne g sur M n telle que l'inégalité suivante soit vérifiée, n 2 ( n − 2 ) n − 1 C < R g ⩽ n ( n − 1 ) C , si et seulement si M n est difféomorphe à la sphère S n ." @default.
- W2008199944 created "2016-06-24" @default.
- W2008199944 creator A5058857113 @default.
- W2008199944 date "2011-02-01" @default.
- W2008199944 modified "2023-10-17" @default.
- W2008199944 title "A sphere theorem for pinching positive scalar curvature manifolds" @default.
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- W2008199944 doi "https://doi.org/10.1016/j.matpur.2010.08.002" @default.
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