Let $M$ be a compact Riemmanian manifold. Let $G$ denote the set of all geodesics of $M$. If $\gamma\in G$ let $l(\gamma)$ denote its length. Let $S=\sup\{l(\gamma): \gamma\in G\}$
Suppose $S<\infty$. How can we estimate $S$ geometrically?
Edit: I changed some assumptions.
Thanks