
This article is cited in 1 scientific paper (total in 1 paper)
Some results on Riemannian $g$natural metrics generated by classical lifts on the tangent bundle
L. Bilen^{a}, A. Gezer^{b} ^{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 threefold. 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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MSC: 53C07, 53B20, 53C21 Received: 27.07.2016 Revised: 07.09.2016
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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 1834
\mathnet{http://mi.mathnet.ru/emj274}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000429192500002}
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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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