Journal of the Mathematical Society of Japan

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

Toshiaki ADACHI, Sadahiro MAEDA, and Masakazu YAMAGISHI

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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 tan2r is rational or irrational. Each length spectrum is simple when tan2r is irrationaj but when tan2r 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

Permanent link to this document
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
Primary: 53C22: Geodesics [See also 58E10]
Secondary: 53C40: Global submanifolds [See also 53B25]

Keywords
geodesic sphere length spectrum real hypersurfaces complex space form

Citation

ADACHI, Toshiaki; MAEDA, Sadahiro; YAMAGISHI, Masakazu. Length spectrum of geodesic spheres in a non-flat complex space form. J. Math. Soc. Japan 54 (2002), no. 2, 373--408. doi:10.2969/jmsj/05420373. https://projecteuclid.org/euclid.jmsj/1213024073


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