Morse concavity for closed geodesics (Q981057)

\textit{M. Morse} [The calculus of variations in the large. (American Mathematical Society Colloquium Publ. 18) New York: American Mathematical Society (AMS) (1934; Zbl 0011.02802)] studied the indices of a closed geodesic \(\gamma\) on a Riemannian manifold. The concavity of \(\gamma\) is defined as the difference between the index of \(\gamma\) in the free loop space and the index of \(\gamma\) in the pointed loop space. Many authors studied multiplicity and stability of closed orbits when the Morse indices of the prime closed orbits were not too small. In this paper, the authors study the Morse concavity forms of closed geodesics, and obtain more information related to the Morse indices of prime closed geodesics on Finsler and Riemannian manifolds.