Streil, Manuel (2017) Pinching the Sectional Curvature on Open Manifolds. JOURNAL OF GEOMETRIC ANALYSIS, 27 (3). pp. 2224-2234. ISSN 1050-6926, 1559-002X
Full text not available from this repository. (Request a copy)Abstract
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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; Open manifolds; Gromov's h-principle; Curvature relations; Pinching |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Dec 2018 13:16 |
| Last Modified: | 18 Feb 2019 15:22 |
| URI: | https://pred.uni-regensburg.de/id/eprint/1618 |
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