Topology of Co-symplectic/Co-Kähler Manifolds

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,

Theorem. Co-symplectic manifold = Symplectic mapping torus; Co-Kähler manifold = Kähler mapping torus.

Keywords

Co-symplectic manifold, symplectic mapping torus, co-Kähler manifold, Kähler mapping torus

2010 Mathematics Subject Classification

Primary 53C15. Secondary 53C55, 53D35, 57R17.

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Published 1 January 2008