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Zh. Mat. Fiz. Anal. Geom., 2015, Volume 11, Number 2, Pages 159–173 (Mi jmag614)  

This article is cited in 4 scientific papers (total in 4 papers)

Properties of Modified Riemannian Extensions

A. Gezera, L. Bilenb, A. Cakmaka

a Ataturk University, Faculty of Science, Department of Mathematics, 25240, Erzurum-Turkey
b Igdir University, Igdir Vocational School, 76000, Igdir-Turkey

Abstract: Let $M$ be an $n$-dimensional differentiable manifold with a symmetric connection $\nabla $ and $T^{\ast }M$ be its cotangent bundle. In this paper, we study some properties of the modified Riemannian extension $\widetilde{g}_{\nabla ,c}$ on $T^{\ast }M$ defined by means of a symmetric $(0,2)$-tensor field $c$ on $M.$ We get the conditions under which $T^{\ast }M $ endowed with the horizontal lift $^{H}J$ of an almost complex structure $J$ and with the metric $\widetilde{g}_{\nabla ,c}$ is a Kähler–Norden manifold. Also curvature properties of the Levi–Civita connection of the metric $\widetilde{g}_{\nabla ,c}$ are presented.

Key words and phrases: cotangent bundle, Kähler–Norden manifold, modified Riemannian extension, Riemannian curvature tensors, semi-symmetric manifold.

DOI: https://doi.org/10.15407/mag11.02.159

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Bibliographic databases:

MSC: 53C07, 53C55, 53C35
Received: 21.01.2014
Revised: 16.12.2014
Language:

Citation: A. Gezer, L. Bilen, A. Cakmak, “Properties of Modified Riemannian Extensions”, Zh. Mat. Fiz. Anal. Geom., 11:2 (2015), 159–173

Citation in format AMSBIB
\Bibitem{GezBilCak15}
\by A.~Gezer, L.~Bilen, A.~Cakmak
\paper Properties of Modified Riemannian Extensions
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2015
\vol 11
\issue 2
\pages 159--173
\mathnet{http://mi.mathnet.ru/jmag614}
\crossref{https://doi.org/10.15407/mag11.02.159}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3442843}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000354621000003}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. C.-L. Bejan, S. Eken, “A harmonic endomorphism in a semi-Riemannian context”, Proceedings of the Seventeenth International Conference on Geometry, Integrability and Quantization, eds. I. Mladenov, G. Meng, A. Yoshioka, Inst. Biophysics & Biomedical Engineering Bulgarian Acad. Sciences, 2016, 172–181  crossref  mathscinet  isi
    2. C.-L. Bejan, S. Eken, “A characterization of the Riemann extension in terms of harmonicity”, Czech. Math. J., 67:1 (2017), 197–206  crossref  mathscinet  zmath  isi  scopus
    3. L. Bilen, A. Gezer, “On metric connections with torsion on the cotangent bundle with modified Riemannian extension”, J. Geom., 109:1 (2018), UNSP 6  crossref  mathscinet  isi  scopus
    4. H. Cayir, “Sasakian metrics, integrability conditions and operators on cotangent bundle”, Honam Math. J., 40:4 (2018), 749–763  crossref  mathscinet  zmath  isi
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