I also got involved with geodesics on surfaces. I gave the first examples of compact surfaces with focal points but no conjugate points . Leon Green and I showed that a compactly supported perturbation of the Euclidean plane which has no conjugate points is isometric to the plane . This work was later extended by Chris Croke.
. On the Variety of Manifolds without Conjugate Points, Trans.
Amer. Math. Soc. 210, 185-201 (1975).
. Planes without Conjugate Points, (with Leon Green), J. Differential Geom. 22, 43-47 (1985).