Ricci curvatures of contact Riemannian manifolds (Q1109349)
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scientific article; zbMATH DE number 4069746
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Ricci curvatures of contact Riemannian manifolds |
scientific article; zbMATH DE number 4069746 |
Statements
Ricci curvatures of contact Riemannian manifolds (English)
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1988
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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.
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Sasakian manifold
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Einstein manifold
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Ricci curvature
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contact Riemannian manifold
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