Compact flat Riemannian manifolds
نویسندگان
چکیده
منابع مشابه
The Calabi Construction for Compact Ricci Flat Riemannian Manifolds
1. The main result and some consequences. In 1956 E. Calabi [6] attacked the classification problem of compact euclidean space forms by means of a special construction, called the Calabi construction (see Wolf [14, p. 124]). Here we announce that the construction can be extended to compact riemannian manifolds whose Ricci curvature tensor is zero (Ricci flat). Of course, it is not known if ther...
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where k is the first Betti number b^M), T is a flat riemannian λ -torus, M~ is a compact connected Ricci-flat (n — λ;)-manifold, and Ψ is a finite group of fixed point free isometries of T x M' of a certain sort (Theorem 4.1). This extends Calabi's result on the structure of compact euclidean space forms ([7] see [20, p. 125]) from flat manifolds to Ricci-flat manifolds. We use it to essentiall...
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M is said to have positive curvature operators if the eigenvalues of Z are positive at each point p € M. Meyer used the theory of harmonic forms to prove that a compact oriented n-dimensional Riemannian manifold with positive curvature operators must have the real homology of an n-dimensional sphere [GM, Proposition 2.9]. Using the theory of minimal two-spheres, we will outline a proof of the f...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1972
ISSN: 0022-040X
DOI: 10.4310/jdg/1214430500