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Pinching the Sectional Curvature on Open Manifolds

Streil, Manuel


We sharpen Gromov's well-known and surprising result that any smooth open manifold M admits (generally incomplete) Riemannian metrics with strictly positive sectional curvature as well as ones with strictly negative curvature by showing that any such M indeed also supports metrics which are arbitrarily pinched. This result is actually also optimal, since for the existence of constant sectional ...


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