Reduction of coKähler and 3-cosymplectic manifolds

The notions of coKähler manifolds and 3-cosymplectic manifolds are odd-dimensional analogues of the ones of Kähler manifolds and hyperKähler manifolds, respectively. In this paper, we obtain reduction theorems of coKähler manifolds and 3-cosymplectic manifolds. We show that Kähler and coKähler (hyperKähler and 3-cosymplectic) reductions admit a natural compatibility with respect to ``cylinder constructions". We further prove the compatibility of Kähler and coKähler reductions with respect to the “mapping torus construction”.