Asymptotic behaviour of length spectrum of circles on non-flat complex space forms

Abstract

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 $\lambda$.