Symplectic real Bott manifolds
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Abstract:
A real Bott manifold is the total space of an iterated $\mathbb {R}P^1$-bundle over a point, where each $\mathbb {R}P^1$-bundle is the projectivization of a Whitney sum of two real line bundles. In this paper, we characterize real Bott manifolds which admit a symplectic form. In particular, it turns out that a real Bott manifold admits a symplectic form if and only if it is cohomologically symplectic. In this case, it admits even a Kähler structure. We also prove that any symplectic cohomology class of a real Bott manifold can be represented by a symplectic form. Finally, we study the flux of a symplectic real Bott manifold.References
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Additional Information
- Hiroaki Ishida
- Affiliation: Graduate School of Science, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
- MR Author ID: 938837
- Email: hiroaki.ishida86@gmail.com
- Received by editor(s): January 19, 2010
- Received by editor(s) in revised form: July 29, 2010
- Published electronically: January 13, 2011
- Communicated by: Jon G. Wolfson
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 3009-3014
- MSC (2010): Primary 57R17, 57S25
- DOI: https://doi.org/10.1090/S0002-9939-2011-10729-9
- MathSciNet review: 2801640