Isometry-invariant geodesics on spheres
For most closed Riemannian manifolds any isometry will have infinitely many invariant geodesics for topological reasons [cf. the reviewer and \textit{S. Halperin}, Publ. Math., Inst. Hautes Etud. Sci. 56, 171-178 (1982; Zbl 0508.55013)]. This is not the case for the simplest manifolds such as e.g. spheres, where indeed for the standard metric almost any isometry will have only finitely many invariant geodesics. In contrast, however, the author proves the interesting result that (finite order) isometries for generic metrics of spheres have infinitely many invariant geodesics.
scientific article; zbMATH DE number 4092285
scientific article