Cartan-Hadamard theorem: Difference between revisions
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{{sectional curvature result}} | {{sectional curvature result}} | ||
{{relating curvature to topology}} | |||
{{universal cover prediction}} | |||
==Statement== | ==Statement== | ||
Any [[negatively curved manifold]], viz any manifold which has negative sectional curvature everywhere, has the property that its universal cover is diffeomorphic to real Euclidean space. | Any [[negatively curved manifold]], viz any manifold which has negative sectional curvature everywhere, has the property that its universal cover is diffeomorphic to real Euclidean space. | ||
Revision as of 05:16, 11 May 2007
This article describes a result related to the sectional curvature of a Riemannian manifold
This result relates information on curvature to information on topology of a manifold
This article makes a prediction about the universal cover of a manifold based on given data at the level of a:[[{{{1}}}]][[Category: Results predicting the universal cover at the level of {{{1}}}]]
Statement
Any negatively curved manifold, viz any manifold which has negative sectional curvature everywhere, has the property that its universal cover is diffeomorphic to real Euclidean space.