Morse-Sard theorem for closed geodesics
Jiří Souček · Czech digital mathematics library · 1984
The existence of finite or infinite number of closed geodesies on a compact Riemannian manifold can be proved under suitable assumptions.The paper brings another type of information.It is proved here that the set V of lengths of all closed geodesies on a real-analytic compact Rieraann manifold is always a discrete set.The proof is based on a version of Morse-Sard theorem for real-analytic maps.