Self-orthogonal foliate conformal symplectic almost para-Hermitian manifolds (Q1897580)

Let \(M = M(J, \Omega, g)\) be a \(2m\)-dimensional almost para-Hermitian manifold in the sense of \textit{P. Libermann} [Ann. Mat. Pura Appl., IV. Ser. 36, 27-120 (1954; Zbl 0056.154)]. The authors give a sufficient condition for \(M\) to have a locally conformal symplectic structure. Then they prove that \(M\) is locally a product \(M_S \times M_{S^*}\) for which \(M_S\) and \(M_{S^*}\) are self-orthogonal \(m\)-dimensional submanifolds of \(M\). Moreover, \(M\) is Ricci flat and if \(X_{\text{Ric}}\) denotes the dual vector field with respect to the 2-form \(\Omega\) of the Ricci 1-form \(\theta_{\text{Ric}}\), then \(X_{\text{Ric}}\) defines a relative infinitesimal conformal transformation of \(\Omega\).