Gromov–Witten Invariants on the Products of Almost Contact Metric Manifolds

Abstract

We investigate Gromov–Witten invariants and quantum cohomologies on the products of almost contact metric manifolds. The product of two cosymplectic manifolds has a Kahler structure. We compute some cohomology classes of compact cosymplectic manifolds and show that any compact simply connected Kahler manifold cannot be a product of two cosymplectic manifolds. On the products we get some geometric properties, Gromov–Witten invariants and quantum cohomologies. We have some relations between Gromov–Witten invariants of the products and the ones of two cosymplectic manifolds.