Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2021; 36(1): 135-147

Online first article December 22, 2020      Printed January 31, 2021

https://doi.org/10.4134/CKMS.c190423

Copyright © The Korean Mathematical Society.

$g$-natural metric and harmonicity on the cotangent bundle

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