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Distribution of length spectrum of circles on a complex hyperbolic space

Published online by Cambridge University Press:  22 January 2016

Toshiaki Adachi
Toshiaki Adachi*
Affiliation:
Department of Mathematics, Nagoya Institute of Technology, Gokiso, Showa-ku, Nagoya 466-8555, Japan, adachi@math.kyy.nitech.ac.jp
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Abstract

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It is well-known that all geodesics on a Riemannian symmetric space of rank one are congruent each other under the action of isometry group. Being concerned with circles, we also know that two closed circles in a real space form are congruent if and only if they have the same length. In this paper we study how prime periods of circles on a complex hyperbolic space are distributed on a real line and show that even if two circles have the same length and the same geodesic curvature they are not necessarily congruent each other.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 153 , 1999 , pp. 119 - 140
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1999

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