On a classification of Killing vector fields on a tangent bundle with g-natural metric
Differential Geometry
2013-05-17 v1
Abstract
The tangent bundle of a Riemannian manifold (M,g) with non-degenerated g-natural metric G that admits a Killing vector field is investigated. Using Taylor's formula (TM,G) is decomposed into four classes that are investigated separately. The equivalence of the existence of Killing vector field on M and TM is proved. Key words: Riemannian manifold, tangent bundle, g-natural metric, Killing vector field, non-degenerate metric.
Keywords
Cite
@article{arxiv.1305.3871,
title = {On a classification of Killing vector fields on a tangent bundle with g-natural metric},
author = {Stanisław Ewert-Krzemieniewski},
journal= {arXiv preprint arXiv:1305.3871},
year = {2013}
}
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43 pages