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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 $$M\times M$$.
##### MSC:
 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53D15 Almost contact and almost symplectic manifolds
##### Keywords:
locally conformal cosymplectic structure
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