Pinching on open manifolds
Differential Geometry
2010-09-16 v1
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.
Cite
@article{arxiv.1009.2912,
title = {Pinching on open manifolds},
author = {Manuel Streil},
journal= {arXiv preprint arXiv:1009.2912},
year = {2010}
}