Topology of Co-symplectic/Co-Kähler Manifolds

Abstract

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.