A note on the scalar curvature of a compact Riemannian manifold
Abstract
In the present paper, we formulate conditions for the constancy of the scalar curvature of an -dimensional compact Riemannian manifold . In particular, conditions for the constancy of the scalar curvature of in the case of the quasi-negative Ricci tensor are found. Conditions are also obtained for a compact Riemannian manifold to be an Einstein manifold.
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