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Ricci curvatures of contact Riemannian manifolds. (English) Zbl 0655.53035

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.
Reviewer: K.Ogiue

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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