The integral of the scalar curvature of complete manifolds without conjugate points (Q1204878)

The main result of the paper states that, on a complete Riemannian manifold \(M\) without conjugate points and integrable (on the unit tangent bundle) positive or negative part of the Ricci curvature, the integral of the scalar curvature is non-positive and, unless \(M\) is flat, strictly negative. This generalises results of E. Hopf, Green and others.