On deformed-Sasaki metric and harmonicity in tangent bundles
Commun. Korean Math. Soc. 2020 Vol. 35, No. 3, 1019-1035
Published online July 2, 2020
Printed July 31, 2020
Naima Boussekkine, Abderrahim Zagane
University Center of Relizane; University Center of Relizane
Abstract : 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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