In this paper, we study length spectrum of circles on a complex projective space and on a complex hyperbolic space. In particular, we focus ourselves on the asymptotic behaviour of the number of congruency classes of circles with length $\lambda$ and on the asymptotic behaviour of the number of congruency classes of circles of prescribed geodesic curvature with length not greater than $\lambda$.
"Asymptotic behaviour of length spectrum of circles on non-flat complex space forms." Proc. Japan Acad. Ser. A Math. Sci. 76 (5) 60 - 65, May 2000. https://doi.org/10.3792/pjaa.76.60