Ricci curvatures of contact Riemannian manifolds
Copyright policy )Ricci curvatures of contact Riemannian manifolds
It is not known whether there exist contact Riemannian manifolds of constant \(\phi\)-sectional curvature which are not Sasakian. The author proves that the Ricci curvature of a contact Riemannian manifold of constant \(\phi\)-sectional curvature satisfies an inequality, from which a condition for such a manifold to be Sasakian is obtained. He also gives a condition for an Einstein contact Riemannian manifold to be Sasakian.
53C15, Ricci curvature, Special Riemannian manifolds (Einstein, Sasakian, etc.), contact Riemannian manifold, Einstein manifold, General geometric structures on manifolds (almost complex, almost product structures, etc.), 53C25, Sasakian manifold
53C15, Ricci curvature, Special Riemannian manifolds (Einstein, Sasakian, etc.), contact Riemannian manifold, Einstein manifold, General geometric structures on manifolds (almost complex, almost product structures, etc.), 53C25, Sasakian manifold
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