Pinching on open manifolds

Manuel Streil

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arXiv · 1009.2912

Pinching on open manifolds

Manuel Streil

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Abstract

We show that the 2-jet bundle of local Riemannian metrics on an arbitrary differentiable manifold admits a section which pointwise fulfills the curvature relation sec(g)=a for any real number a. It follows by Gromov's h-principle for open, invariant differential relations that every noncompact differentiable manifold carries arbitrarily pinched (incomplete) Riemannian metrics.

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Manuel Streil. 2010-09-15. Pinching on open manifolds. https://arxiv.org/abs/1009.2912

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