On the structure of co-Kähler manifolds

2012/09/15 by Giovanni Bazzoni, Bazzoni, Giovanni, John Oprea +1 · 1 citation
Mathematics · Medicine · #53C25 #Biomedical Research and Pathophysiology #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · doi:10.48550/arxiv.1209.3373

openalex publication_date 2012/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By the work of Li, a compact co-Kähler manifold M is a mapping torus K_φ, where K is a Kähler manifold and φ is a Hermitian isometry. We show here that there is always a finite cyclic cover M of the form M ≅ K × S¹, where ≅ is equivariant diffeomorphism with respect to an action of S¹ on M and the action of S¹ on K × S¹ by translation on the second factor. Furthermore, the covering transformations act diagonally on S¹, K and are translations on the S¹ factor. In this way, we see that, up to a finite cover, all compact co-Kähler manifolds arise as the product of a Kähler manifold and a circle.

Citations

• Aspherical Kähler Manifolds with Solvable Fundamental Group

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• Cosymplectic Chern--Hamilton conjecture

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