Walker manifolds and Killing magnetic curves

On a Walker manifold Mf3, we first characterize the Killing vector fields, aiming to obtain the corresponding Killing magnetic curves. When the manifold is endowed with a unitary spacelike vector field ξ, we prove that after a reparameterization, any lightlike curve normal to ξ is a lightlike geodes...

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Bibliographic Details
Published inDifferential geometry and its applications Vol. 35; pp. 106 - 116
Main Authors Bejan, Cornelia-Livia, Druţă-Romaniuc, Simona-Luiza
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.09.2014
Subjects
Killing vector field
Lightlike geodesic
Magnetic field
Magnetic trajectory
Walker manifold
Killing vector field
Walker manifold
Magnetic field
Lightlike geodesic
Magnetic trajectory
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Summary:On a Walker manifold Mf3, we first characterize the Killing vector fields, aiming to obtain the corresponding Killing magnetic curves. When the manifold is endowed with a unitary spacelike vector field ξ, we prove that after a reparameterization, any lightlike curve normal to ξ is a lightlike geodesic. We also show that on Mf3, equipped with a Killing vector field V, any arc length parameterized spacelike or timelike curve, normal to V, is a magnetic trajectory associated to V. We characterize the normal magnetic curves corresponding to some Killing vector fields on Mf3, obtaining their explicit expressions for certain functions f.
ISSN:0926-2245
1872-6984
DOI:10.1016/j.difgeo.2014.03.001