Nil happens. What about Sol?

2012/07/06 by T. Tâm Nguyễn Phan, T. Tam Nguyen Phan, Phan, T. Tam Nguyen
Earth and Planetary Sciences · Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Marine and environmental studies #math.DG

paper · pdf · doi:10.48550/arxiv.1207.1734

2 pages

arxiv created 2012/07/06 · openalex publication_date 2012/07/06 · arxiv updated 2012/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct complete, finite volume, 4-dimensional manifolds with sectional curvature -1<K<0 with cusp cross sections compact solvmanifolds.

Citations

• Pinched smooth hyperbolization

Related

• Fundamental groups of finite volume, bounded negatively curved 4-manifolds are not 3-manifold groups
• Stability, Finiteness and Dimension Four
• Dissolving four-manifolds and positive scalar curvature
• Examples of Riemannian Manifolds with non-negative sectional curvature
• Collapsing 4-manifolds under a lower curvature bound