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 Eurasian Math. J., 2017, Volume 8, Number 4, Pages 18–34 (Mi emj274)

Some results on Riemannian $g$-natural metrics generated by classical lifts on the tangent bundle

L. Bilena, A. Gezerb

a Department of Mathematics and Computer Science, Igdir University, 76000 Igdir, Turkey
b Department of Mathematics, Ataturk University, 25240 Erzurum, Turkey

Abstract: Let $(M, g)$ be an $n$-dimensional Riemannian manifold and $TM$ its tangent bundle equipped with Riemannian $g$-natural metrics which are linear combinations of the three classical lifts of the base metric with constant coefficients. The purpose of the present paper is three-fold. Firstly, to study conditions for the tangent bundle $TM$ to be locally conformally flat. Secondly, to define a metric connection on the tangent bundle $TM$ with respect to the Riemannian $g$-natural metric and study some its properties. Finally, to classify affine Killing and Killing vector fields. on the tangent bundle $TM$.

Keywords and phrases: affine Killing and Killing vector fields, conformal curvature tensor, Riemannian $g$-natural metric, metric connection, tangent bundle.

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Bibliographic databases:
MSC: 53C07, 53B20, 53C21
Revised: 07.09.2016
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Citation: L. Bilen, A. Gezer, “Some results on Riemannian $g$-natural metrics generated by classical lifts on the tangent bundle”, Eurasian Math. J., 8:4 (2017), 18–34

Citation in format AMSBIB
\Bibitem{BilGez17}
\by L.~Bilen, A.~Gezer
\paper Some results on Riemannian $g$-natural metrics generated by classical lifts on the tangent bundle
\jour Eurasian Math. J.
\yr 2017
\vol 8
\issue 4
\pages 18--34
\mathnet{http://mi.mathnet.ru/emj274}

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This publication is cited in the following articles:
1. D. D'Ascanio, P. B. Gilkey, P. Pisani, “Affine killing vector fields on homogeneous surfaces with torsion”, Class. Quantum Gravity, 36:14 (2019), 145008
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