Length spectrum of circles in a complex projective space
type: Item
instance of: scholarly article
title: Length spectrum of circles in a complex projective space
zbMATH Open document ID: 0909.53041
author: Toshiaki Adachi
author: Sadahiro Maeda
published in: Osaka Journal of Mathematics
publication date: 1999-03-25T00:00:00Z
review text: A circle with geodesic curvature \(\kappa\geq 0\) is a curve \(\gamma\) parametrized by arc-length in a Riemannian manifold and satisfying the equation \[ \nabla_t\nabla_t\dot\gamma(t)=-\kappa^2\dot\gamma(t). \] The authors restrict themselves to the complex projective space. They consider the set of prime periods of periodic circles and show that it coincides with the real positive line. If the geodesic curvature is kept fixed, then they show that this set is discrete and unbounded. If what the authors call complex torsion \(\tau\) is kept fixed and \(\kappa\) not, the set of prime periods is also discrete and unbounded. They calculate the smallest possible prime period if \(\kappa\) or \(\tau\) is kept fixed.
reviewed by: Gudlaugur Thorbergsson
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 1216671
zbMATH Keywords: circles
zbMATH Keywords: complex projective space
zbMATH Keywords: periodic circles
zbMATH Keywords: complex torsion
zbMATH Keywords: prime periods
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1216671