Four-manifolds with 1/4-pinched Flag Curvatures
نویسندگان
چکیده
منابع مشابه
Classification of Manifolds with Weakly 1/4-pinched Curvatures Simon Brendle and Richard Schoen
A classical theorem due to M. Berger [2] and W. Klingenberg [11] states that a simply connected Riemannian manifold whose sectional curvatures all lie in the interval [1, 4] is either isometric to a symmetric space or homeomorphic to Sn (see also [12], Theorems 2.8.7 and 2.8.10). In this paper, we provide a classification, up to diffeomorphism, of all Riemannian manifolds whose sectional curvat...
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A generalized flag manifold is a homogeneous space of the form G/K, where K is the centralizer of a torus in a compact connected semisimple Lie group G. We classify all flag manifolds with four isotropy summands by the use of t-roots. We present new G-invariant Einstein metrics by solving explicity the Einstein equation. We also examine the isometric problem for these Einstein metrics. 2000 Mat...
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In this lecture we will describe our recent joint work with SimonBrendle ([1], [2]) in which we give the differentiable classification ofcompact Riemannian manifolds with pointwise 1/4-pinched curvature.Our theorems are:Theorem 1. Let M be a compact Riemannian manifold with pointwise1/4-pinched curvature. Then M admits a metric of constant curvature,and therefore is ...
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In this note, we will show that the fundamental group of any negatively δ-pinched (δ > 14) manifold can’t be the fundamental group of a quasi-compact Kähler manifold. As a consequence of our proof, we also show that any nonuniform lattice in F4(−20) cannot be the fundamental group of a quasi-compact Kähler manifold. The corresponding result for uniform lattices was proved by Carlson and Hernánd...
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ژورنال
عنوان ژورنال: Asian Journal of Mathematics
سال: 2009
ISSN: 1093-6106,1945-0036
DOI: 10.4310/ajm.2009.v13.n2.a5