Ricci curvature for conjugate and focal points on GRW space-times (Q2732153)

The authors' working space is a warped product \((n + 1)\)-dimensional Generalized Robertson-Walker (GRW) spacetime \(M\), with an \(n\)-dimensional fiber space \(F\) and a warped function \(f\). By computing the Ricci curvature of \(M\), they obtain two conditions for the conjugate points which appear as the two different inequalities of the warping function \(f\). Using those two conditions, they further obtain a lower bound of the length of a unit timelike geodesic for focal points emanating from the graph over the spacelike fiber \(F\) in \(M\).