$g$-natural metric and harmonicity on the cotangent bundle
Commun. Korean Math. Soc. 2021 Vol. 36, No. 1, 135-147
https://doi.org/10.4134/CKMS.c190423
Published online December 22, 2020
Printed January 31, 2021
Abderrahim Zagane, Mohammed Zagane
University Center of Relizane; University Mustapha Stambouli of Mascara
Abstract : In this paper, we introduce the harmonicity of a covector field on a Riemannian manifold $(M,g)$ to its cotangent bundle $T^{\ast}M$ equipped with $g$-natural metric. Afterward we also construct some examples of harmonic covector fields.
Keywords : Horizontal lift, vertical lift, cotangent bundles, $g$-natural metric, harmonic maps
MSC numbers : 53A45, 53C20, 58E20
Supported by : Partially supported by the Algerian National Research Agency PRFU and GMFAMI Laboratories
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