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On Riemannian manifolds endowed with a locally conformal cosymplectic structure. (English) Zbl 1104.53025
Authors’ abstract: We deal with a locally conformal cosymplectic manifold \(M(\phi ,\Omega ,\xi ,\eta ,g)\) admitting a conformal contact quasi-torse-forming vector field \(T\). The presymplectic \(2\)-form \(\Omega\) is a locally conformal cosymplectic \(2\)-form. It is shown that \(T\) is a \(3\)-exterior concurrent vector field. Infinitesimal transformations of the Lie algebra of \(\bigwedge M\) are investigated. The Gauss map of the hypersurface \(M_\xi\) normal to \(\xi\) is conformal and \(M_\xi \times M_\xi\) is a Chen submanifold of \(M\times M\).
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53D15 Almost contact and almost symplectic manifolds
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