## Journal of the Mathematical Society of Japan

### Length spectrum of geodesic spheres in a non-flat complex space form

#### Abstract

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 $r$ in a complex projective space of holomorphic sectional curvature 4 is quite different according as $\tan^{2}r$ is rational or irrational. Each length spectrum is simple when $\tan^{2}r$ is irrationaj but when $\tan^{2}r$ is rationaj it is not necessarily simple and moreover the multiplicity is not uniformly bounded.

#### Article information

Source
J. Math. Soc. Japan, Volume 54, Number 2 (2002), 373-408.

Dates
First available in Project Euclid: 9 June 2008

https://projecteuclid.org/euclid.jmsj/1213024073

Digital Object Identifier
doi:10.2969/jmsj/05420373

Mathematical Reviews number (MathSciNet)
MR1883524

Zentralblatt MATH identifier
1037.53019

Subjects