Geometriae Dedicata

, Volume 148, Issue 1, pp 3–14 | Cite as

Taming 3-manifolds using scalar curvature

Original Paper
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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 \({\mathbb{R}^3}\) 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.

Keywords

Positive scalar curvature Noncompact manifolds Whitehead manifold 

Mathematics Subject Classification (2000)

53C21 19K56 57N10 57M40 
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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of MathematicsWellesley CollegeWellesleyUSA
  2. 2.Department of MathematicsUniversity of ChicagoChicagoUSA
  3. 3.Department of MathematicsVanderbilt UniversityNashvilleUSA

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