Circles in Riemannian symmetric spaces
Circles in Riemannian manifolds are defined by means of the canonical covariant derivative analogously to the standard circles in Euclidean spaces. The aim of this paper is to extend earlier results [see \textit{T. Adachi}, J. Math. Soc. Japan 48, 205-227 (1996; Zbl 0867.53048) and \textit{T. Adachi} and \textit{S. Maeda}, Tsukuba J. Math. 21, 29-42 (1997; Zbl 0891.53036)] to circles in compact Riemannian symmetric spaces. The main theorem says that every circle in such a space of rank one is the orbit of a one-parameter subgroup of isometries. Moreover, all homogeneous spaces with this property are either Riemannian globally symmetric spaces of rank one or Euclidean spaces.
scientific article; zbMATH DE number 1333295