Taming 3-manifolds using scalar curvature

Author: Chang Stanley  

Publisher: Springer Publishing Company

ISSN: 0046-5755

Source: Geometriae Dedicata, Vol.148, Iss.1, 2010-10, pp. : 3-14

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Abstract

In this paper we address the issue of uniformly positive scalar curvature on noncompact 3-manifolds. In particular we show that the Whitehead manifold lacks such a metric, and in fact that $${mathbb{R}^3}$$</EquationSource> is the only contractible noncompact 3-manifold with a metric of uniformly positive scalar curvature. We also describe contractible noncompact manifolds of higher dimension exhibiting this curvature phenomenon. Lastly we characterize all connected oriented 3-manifolds with finitely generated fundamental group allowing such a metric.