A comparison theorem on sectors for Kähler magnetic fields
type: Item
instance of: scholarly article
title: A comparison theorem on sectors for Kähler magnetic fields
zbMATH Open document ID: 1090.53060
author: Toshiaki Adachi
published in: Proceedings of the Japan Academy. Series A
publication date: 2006-02-21T00:00:00Z
review text: Let \((M,J,< >)\) be a Kähler manifold. We call a constant multiple \(B_k = hB_J\) of the Kähler form \(B_J\) on \(M\), a Kähler magnetic field. A vector field \(Y\) along a trajectory \(\nu\) for \(B_J\) is said to be a normal magnetic Jacobi field for \(B_k\) if it satisfies \[ \nabla_{\dot{\nu}}\nabla_{\dot{\nu}}Y - kJ\nabla_{\dot{\nu}}Y + R(Y,\dot{\nu}) = 0; \;\;\nabla_{\dot{\nu}} \perp \dot{\nu}, \] where \(R\) denotes the curvature tensor on \(M\). The author proves some comparision theorem on magnetic Jacobi fields and studies the lengths of arcs for sectors.
reviewed by: Constantin Călin
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 5008562
MaRDI profile type: Publication
full work available at URL: pjaa.81.110
OpenAlex ID: W1980732332
cites work: Kähler magnetic flows for a manifold of constant holomorphic sectional curvature
cites work: A comparison theorem on magnetic jacobi fields
cites work: A comparison theorem on crescents for Kähler magnetic fields
cites work: Q4067705
cites work: Magnetic flows of Anosov type
cites work: Totally geodesic immersions of Kähler manifolds and Kähler Frenet curves
DOI: 10.3792/PJAA.81.110
description: scientific article; zbMATH DE number 5008562