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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2020 / Cilt: 69 - Sayı: 1

On generalized Cheeger-Gromoll metric and harmonicity

Abderrahim ZAGANE, Mustapha DJAA, Reda KADA BEN OTMANE

Pages
629–645
DOI
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Abstract

In this paper, we introduce the Generalized Cheeger-Gromoll metric on the tangent bundle TM, as a natural metric on TM. We establish a necessary and sufficient conditions under which a vector field is harmonic with respect to the Generalized Cheeger-Gromoll metric. We also construct some examples of harmonic vector fields.