Zusammenfassung
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 ...
Zusammenfassung
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 curvature metrics on M, even incomplete ones, there are topological obstructions known. The result is proven by observing that using jets of metrics, the pinching problem can be transformed into a differential curvature relation, which makes it feasible to Gromov's general h-principle.
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