Contractible 3-manifold and Positive scalar curvature (I)

2019/01/14 by Wang, Jian · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.04605

Abstract

In this work we prove that the Whitehead manifold has no complete metric of positive scalar curvature. This result can be generalized to the genus one case. Precisely, we show that no contractible genus one 3-manifold admits a complete metric of positive scalar curvature.

Cited by

• Topological Rigidity of Contractible 3-Manifolds and Handlebody Interiors under Nonnegative Scalar Curvature
• Positive curvature conditions on contractible manifolds

Related

• Contractible 3-manifold and Positive scalar curvature (II)
• 3-Manifolds with positive scalar curvature and bounded geometry
• Topological Rigidity and Positive scalar curvature
• Equivariant 3-manifolds with positive scalar curvature
• Scalar Curvature on some Open 3-Manifolds