Communications of the
Korean Mathematical Society CKMS

We present a smooth simply connected closed eight dimensional manifold with distinct symplectic deformation equivalence classes $[[\omega_i]]$, $i=1,2$ such that the symplectic $Z$ invariant, which is defined in terms of the scalar curvatures of almost \k metrics in \cite{KS}, satisfies $Z(M, [[\omega_1]] ) =\infty $ and $Z(M, [[\omega_2]] ) <0$.

Keywords: almost \k metric, scalar curvature, symplectic manifold, symplectic deformation equivalence class

MSC numbers: Primary 53D05, 53C15, 37J05