Document Type
Article
Publication Date
6-1-2014
Publication Title
Geometriae Dedicata
Abstract
By the work of Li, a compact co-Kähler manifold M is a mapping torus Kφ, 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.
Repository Citation
Bazzoni, Giovanni and Oprea, John, "On The Structure of Co-Kähler Manifolds" (2014). Mathematics and Statistics Faculty Publications. 211.
https://engagedscholarship.csuohio.edu/scimath_facpub/211
DOI
10.1007/s10711-013-9869-7
Version
Postprint
Publisher's Statement
The final publication is available at Springer via http://dx.doi.org/10.1007/s10711-013-9869-7
Volume
170
Issue
1
Comments
The first author thanks the Department of Mathematics at Cleveland State University for its hospitality during his extended visit (funded by CSIC and ICMAT) to Cleveland. In addition, the first author was partially supported by Project MICINN (Spain) MTM2010-17389. The second author was partially supported by a grant from the Simons Foundation: (#244393 to John Oprea).