Pinching on open manifolds

arXiv1009.2912MaRDI QIDQ6220688

Publication date: 15 September 2010

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.

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

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