Finsler manifolds without conjugate points and with integral Ricci curvature (Q1760349)

For a given complete Finsler manifold without conjugate points, the author first extends the Riccati inequality techniques for the trace of the stable Jacobi tensor and then proves a rigidity theorem for complete Finsler manifolds without conjugate points which states that the integral of the Ricci curvature on the unit tangent bundle \(SM\) of a complete Finsler manifold \(M\) without conjugate points is nonpositive and vanishes only if \(M\) is flat, provided that the Ricci curvature on \(SM\) has an integrable positive or negative part.