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Eurasian Mathematical Journal, 2017, Volume 8, Number 4, Pages 18–34
(Mi emj274)
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This article is cited in 2 scientific papers (total in 2 papers)
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.
Received: 27.07.2016 Revised: 07.09.2016
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
Linking options:
https://www.mathnet.ru/eng/emj274 https://www.mathnet.ru/eng/emj/v8/i4/p18
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Abstract page: | 228 | Full-text PDF : | 169 | References: | 43 |
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