Developments around positive sectional curvature
نویسندگان
چکیده
منابع مشابه
Riemannian Manifolds with Positive Sectional Curvature
It is fair to say that Riemannian geometry started with Gauss’s famous ”Disquisitiones generales” from 1827 in which one finds a rigorous discussion of what we now call the Gauss curvature of a surface. Much has been written about the importance and influence of this paper, see in particular the article [Do] by P.Dombrowski for a careful discussion of its contents and influence during that time...
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For a closed manifold M let 9\~(M) (resp. 9\~ic(M)) be thespace of Riemannian metrics on M with positive sectional (resp. Ricci) cur-vature and let Diff(M) be the diffeomorphism group of M, which acts onthese spaces. We construct examples of 7-dimensional manifolds for whichthe moduli space 9\~(M)/ Diff(M) is not connected and others for which9\~c(M)/ Diff(M) has infinitely ...
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We discuss the Sasakian geometry of odd dimensional homotopy spheres. In particular, we give a completely new proof of the existence of metrics of positive Ricci curvature on exotic spheres that can be realized as the boundary of a parallelizable manifold. Furthermore, it is shown that on such homotopy spheres Σ the moduli space of Sasakian structures has infinitely many positive components det...
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ژورنال
عنوان ژورنال: Surveys in Differential Geometry
سال: 2008
ISSN: 1052-9233,2164-4713
DOI: 10.4310/sdg.2008.v13.n1.a4