We investigate the distribution of length of closed geodesics on geodesic spheres and tubes around complex hyperplane in a non-flat complex space form. The feature of the length spectrum of a geodesic sphere of radius in a complex projective space of holomorphic sectional curvature 4 is quite different according as is rational or irrational. Each length spectrum is simple when is irrationaj but when is rationaj it is not necessarily simple and moreover the multiplicity is not uniformly bounded.
Toshiaki ADACHI. Sadahiro MAEDA. Masakazu YAMAGISHI. "Length spectrum of geodesic spheres in a non-flat complex space form." J. Math. Soc. Japan 54 (2) 373 - 408, April, 2002. https://doi.org/10.2969/jmsj/05420373