Symplectic real Bott manifolds

Details Symplectic real Bott manifolds Symplectic real Bott manifolds

2010-01-21

arxiv.org/abs/1001.3726v1

Proc. Amer. Math. Soc. 139 (2011), 3009-3014

Mathematics

Symplectic Geometry

6 pages

Scientific paper

A real Bott manifold is the total space of an iterated $\RP ^1$-bundles over a point, where each $\RP^1$-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 K\"{a}hler structure. We also prove that any symplectic cohomology class of a real Bott manifolds can be represented by a symplectic form. Finally, we study the flux of a symplectic real Bott manifold.

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