Length spectrum of geodesic spheres in rank one symmetric spaces (Q2765978)
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scientific article; zbMATH DE number 1695251
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Length spectrum of geodesic spheres in rank one symmetric spaces |
scientific article; zbMATH DE number 1695251 |
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22 March 2004
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closed geodesics
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length spectrum
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symmetric spaces
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homogeneous submanifolds
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Length spectrum of geodesic spheres in rank one symmetric spaces (English)
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The aim of the present paper is to study the distribution of lengths of closed geodesics on certain homogeneous submanifolds of compact symmetric spaces of rank one, namely of geodesic spheres and tubes around hypersurfaces. The author studies the length spectrum in quite some detail both qualitatively and quantitatively. He makes explicit computations and, in particular, shows cases where all geodesics are simple. The results for complex and quaternionic projective spaces have already been published in previous papers by \textit{T. Adachi} and \textit{S. Maeda} [ Kodai Math. J. 24, 98--119 (2001; Zbl 1032.53044)]{} and by \textit{T. Adachi, S. Maeda} and \textit{M. Yamaguchi} [ J. Math. Soc. Japan 54, 373--408 (2002; Zbl 1037.53019)]. The main new addition is the treatment of the case of the Cayley plane.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00014].
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