Abstract
In this paper we consider the tamed symplectic cone of a compact Hermitian-symplectic manifold. First, we prove a Poincare duality theorem for the tamed symplectic cone. Second, we study the stability of Hermitian-symplectic metrics under the deformation of complex structures and show that the tamed symplectic cones are invariant under the parallel transport with respect to the Gauss–Manin connection.
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