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Topology of co-symplectic/co-Kähler manifolds. (English) Zbl 1170.53014

Summary: Co-symplectic/co-Kähler manifolds are odd dimensional analog of symplectic/Kähler manifolds, defined early by Libermann in 1959/Blair in 1967 respectively. In this paper, we reveal their topology construction via symplectic/Kähler mapping tori. Namely,
\[ \begin{aligned} \text{Theorem.}\quad \text{Co-symplectic manifold} & =\text{Symplectic mapping torus;}\\ \text{Co-Kähler manifold} & = \text{Kähler mapping torus.}\end{aligned} \]

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
53D35 Global theory of symplectic and contact manifolds
57R17 Symplectic and contact topology in high or arbitrary dimension
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