Contractible $3$-manifold and Positive scalar curvature (I)

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.

36 pages, 4 figures, Accepted by JDG

References in corpus (4)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Limit leaves of a CMC lamination are stable
• Contractible 3-manifolds and the double 3-space property

Cited by in corpus (3)

• Positive Scalar Curvature on Noncompact Manifolds and the Liouville Theorem
• Topological Rigidity and Positive scalar curvature
• Scalar Curvature on some Open 3-Manifolds