* On <math>\mathbb{R}^n</math>, there are no conjugate points.
* On Riemannian manifolds with non-positive [[sectional curvature]], there are no conjugate points.
* In [[optimal control]], the sufficient [[Jacobi condition]] states that if there are no conjugate points on the optimal path, then the locally optimal path is unique.<ref>{{cite book |first=Robert F. |last=Stengel |title=Optimal Control and Estimation |___location=New York |publisher=Dover |year=1994 |isbn=0-486-68200-5 |page=215 }}</ref>
