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Commun. Korean Math. Soc. 2020; 35(3): 1019-1035
Online first article July 2, 2020 Printed July 31, 2020
https://doi.org/10.4134/CKMS.c200018
Copyright © The Korean Mathematical Society.
On deformed-Sasaki metric and harmonicity in tangent bundles
Naima Boussekkine, Abderrahim Zagane
University Center of Relizane; University Center of Relizane
In this paper, we introduce the deformed-Sasaki metric on the tangent bundle $TM$ over an $m$-dimensional Riemannian manifold $(M, g)$, as a new natural metric on $TM$. We establish a necessary and sufficient conditions under which a vector field is harmonic with respect to the deformed-Sasaki Metric. We also construct some examples of harmonic vector fields.
Keywords: Horizontal lift and vertical lift, tangent bundles, deformed-Sasaki Metric, harmonic maps
MSC numbers: 53A45, 53C20, 58E20
Supported by: Partially supported by PRFU National Agency Scientific Research of Algeria
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