Open Access
June 2004 On the Killing vector fields of generalized metrics
Rezső L. Lovas
Author Affiliations +
SUT J. Math. 40(2): 133-156 (June 2004). DOI: 10.55937/sut/1108749127

Abstract

We consider a manifold endowed with a metric tensor in its tangent bundle pulled back by its own projection. We shall give necessary and sufficient conditions for a vector field to be an infinitesimal isometry of a metric of this type in general and for some special classes. We also examine translations, i.e., the special class of Killing vector fields whose integral curves are geodesics of an associated Finsler manifold. As applications, we determine the Killing vector fields of Funk metrics, and we give a new proof for the fact that perturbing a Riemannian manifold by a one-form metrically equivalent to a Killing field yields a Randers manifold for which the original vector field is a Killing field as well.

Acknowledgement

I am grateful to my supervisor, Dr. József Szilasi, for fruitful discussions and useful suggestions.

Citation

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Rezső L. Lovas. "On the Killing vector fields of generalized metrics." SUT J. Math. 40 (2) 133 - 156, June 2004. https://doi.org/10.55937/sut/1108749127

Information

Received: 9 September 2004; Published: June 2004
First available in Project Euclid: 18 June 2022

Digital Object Identifier: 10.55937/sut/1108749127

Subjects:
Primary: 53B40

Keywords: Funk metrics , Generalized metrics , Killing vector fields , Randers manifolds , translations

Rights: Copyright © 2004 Tokyo University of Science

Vol.40 • No. 2 • June 2004
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