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April, 2002 Length spectrum of geodesic spheres in a non-flat complex space form
Toshiaki ADACHI, Sadahiro MAEDA, Masakazu YAMAGISHI
J. Math. Soc. Japan 54(2): 373-408 (April, 2002). DOI: 10.2969/jmsj/05420373


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.


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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.


Published: April, 2002
First available in Project Euclid: 9 June 2008

zbMATH: 1037.53019
MathSciNet: MR1883524
Digital Object Identifier: 10.2969/jmsj/05420373

Primary: 53C22
Secondary: 53C40

Keywords: Complex space form , geodesic sphere , length spectrum , Real hypersurfaces

Rights: Copyright © 2002 Mathematical Society of Japan


Vol.54 • No. 2 • April, 2002
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