Examples of Manifolds with Non-negative Sectional Curvature
نویسندگان
چکیده
منابع مشابه
Examples of Riemannian Manifolds with Non-negative Sectional Curvature
Manifolds with non-negative sectional curvature have been of interest since the beginning of global Riemannian geometry, as illustrated by the theorems of Bonnet-Myers, Synge, and the sphere theorem. Some of the oldest conjectures in global Riemannian geometry, as for example the Hopf conjecture on S × S, also fit into this subject. For non-negatively curved manifolds, there are a number of obs...
متن کاملExamples of Manifolds with Non-negative Sectional Curvature
Manifolds with non-negative sectional curvature have been of interest since the beginning of global Riemannian geometry, as illustrated by the theorems of Bonnet-Myers, Synge, and the sphere theorem. Some of the oldest conjectures in global Riemannian geometry, as for example the Hopf conjecture on S × S, also fit into this subject. For non-negatively curved manifolds, there are a number of obs...
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In this paper, we study certain compact 4-manifolds with non-negative sectional curvature K. If s is the scalar curvature and W+ is the self-dual part of Weyl tensor, then it will be shown that there is no metric g on S2 × S2 with both (i) K > 0 and (ii) 1 6 s−W+ ≥ 0. We also investigate other aspects of 4-manifolds with non-negative sectional curvature. One of our results implies a theorem of ...
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In this paper, the authors prove that a strictly Kähler-Berwald manifold with nonzero constant holomorphic sectional curvature must be a Kähler manifold.
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We prove that the space of smooth Riemannian metrics on the three-ball with non-negative Ricci curvature and strictly convex boundary is path-connected; and, moreover, that the associated moduli space (i.e., modulo orientation-preserving diffeomorphisms of the threeball) is contractible. As an application, using results of Maximo, Nunes, and Smith [MNS], we show the existence of properly embedd...
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ژورنال
عنوان ژورنال: Surveys in Differential Geometry
سال: 2006
ISSN: 1052-9233,2164-4713
DOI: 10.4310/sdg.2006.v11.n1.a4