The Jacobi map
type: Item
instance of: scholarly article
title: The Jacobi map
zbMATH Open document ID: 0877.53028
DOI: 10.1016/0393-0440(95)00045-3
author: Jens Chr. Larsen
published in: Journal of Geometry and Physics
publication date: 1996-12-16T00:00:00Z
review text: Using two-parameter variations of a geodesic in a semi-Riemannian manifold, the author introduces \(n\)-th order Jacobi vector fields. He obtains necessary and sufficient conditions for an \(n\)-th order Jacobi field to be the variation vector field as well as the index theorem, giving upper and lower bounds for the focal multiplicity.
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 58E10
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 936182
zbMATH Keywords: geodesic variation
zbMATH Keywords: Jacobi field
zbMATH Keywords: semi-Riemannian manifold
zbMATH Keywords: index theorem
reviewed by: Valery Borisovich Marenich
MaRDI profile type: Publication
full work available at URL: 0393-0440(95)00045-3
OpenAlex ID: W2070388034
cites work: Q4057338
cites work: Geodesics and Jacobi fields in singular semi-riemannian geometry
cites work: Submanifold geometry
cites work: Q3312869
cites work: Q4064107
description: scientific article; zbMATH DE number 936182