Homology Smale-Barden manifolds with K-contact and Sasakian structures

2016/01/22 by Vicente Muñoz, Muñoz, Vicente, Juan Rojo +3
Mathematics · #14J25 #53C25 #53D35 #57R17 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1601.06136

openalex publication_date 2016/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Kollár has found subtle obstructions to the existence of Sasakian structures on 5-dimensional manifolds. In the present article we develop methods of using these obstructions to distinguish K-contact manifolds from Sasakian ones. In particular, we find the first example of a closed 5-manifold M with H₁(M,Z)=0 which is K-contact but which carries no semi-regular Sasakian structures.

Related

• A Smale-Barden manifold admitting K-contact but not Sasakian structure
• Quasi-regular Sasakian and K-contact structures on Smale-Barden manifolds
• A K-contact simply connected 5-manifold with no semi-regular Sasakian\n structure
• Sasakian metrics with an additional contact structure
• Characterization of Sasakian manifolds