Manifolds with nonnegative isotropic curvature
نویسندگان
چکیده
منابع مشابه
Manifolds with Nonnegative Isotropic Curvature
We prove that if (M, g) is a compact locally irreducible Riemannian manifold with nonnegative isotropic curvature, then one of the following possibilities hold: (i) M admits a metric with positive isotropic curvature (ii) (M, g) is isometric to a locally symmetric space (iii) (M, g) is Kähler and biholomorphic to CP n. This is implied by the following two results: (i) Let (M, g) be a compact, l...
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In this short note, as a simple application of the strong result proved recently by Böhm and Wilking, we give a classification on closed manifolds with 2-nonnegative curvature operator. Moreover, by the new invariant cone constructions of Böhm and Wilking, we show that any complete Riemannian manifold (with dimension ≥ 3) whose curvature operator is bounded and satisfies the pinching condition ...
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Let (Mn, g), n ≥ 4, be a compact simply-connected Riemannian manifold with nonnegative isotropic curvature. Given 0 < l ≤ L, we prove that there exists ε = ε(l, L, n) satisfying the following: If the scalar curvature s of g satisfies l ≤ s ≤ L and the Einstein tensor satisfies |Ric − s n g| ≤ ε then M is diffeomorphic to a symmetric space of compact type. This is a smooth analogue of the result...
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ژورنال
عنوان ژورنال: Communications in Analysis and Geometry
سال: 2009
ISSN: 1019-8385,1944-9992
DOI: 10.4310/cag.2009.v17.n4.a2