Circles in a complex projective space
type: Item
instance of: scholarly article
title: Circles in a complex projective space
zbMATH Open document ID: 0857.53034
author: Toshiaki Adachi
author: Sadahiro Maeda
author: Seiichi Udagawa
published in: Osaka Journal of Mathematics
publication date: 1997-03-09T00:00:00Z
review text: In the paper are introduced the notions ``complex torsion of a circle'' and ``prime period of a closed circle'' on the complex space form \(\mathbb{C} P^n(c)\). Using the Hopf fibration \(\pi : S^{2n+1}(1) \to \mathbb{C} P^n(4)\) from a circle \(\gamma\) in \(\mathbb{C} P^n(4)\) with curvature \(k\) one gets a helix \(\widetilde {\gamma}\) with curvature \(k\) and complex torsion \(\tau\) as a horizontal lift of \(\gamma\). The main results are: Theorem 2, where differential equations for \(\widetilde{\gamma}\) are given, and the classification theorem for all circles \(\gamma\) with curvature \(k\), complex torsion \(\tau\) and its prime period.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 871831
zbMATH Keywords: complex projective space
zbMATH Keywords: complex torsion of a circle
zbMATH Keywords: circle
zbMATH Keywords: helix
reviewed by: Grozio Stanilov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 871831