Pinching on open manifolds

Details Pinching on open manifolds Pinching on open manifolds

2010-09-15

arxiv.org/abs/1009.2912v1

Mathematics

Differential Geometry

Scientific paper

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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