• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.1019-1035
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• 2020

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.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.575-592
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• 2021

In this paper, we introduce the Berger type deformed Sasaki metric on the cotangent bundle T^*M over an anti-paraKähler manifold (M, 𝜑, g) as a new natural metric with respect to g non-rigid on T^*M. Firstly, we investigate the Levi-Civita connection of this metric. Secondly, we study the curvature tensor and also we characterize the scalar curvature.

• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.79-95
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• 2023

In this note, we define a Berger type deformed Sasaki metric as a natural metric on the second tangent bundle of a manifold by means of a biparacomplex structure. First, we obtain the Levi-Civita connection of this metric. Secondly, we get the curvature tensor, sectional curvature, and scalar curvature. Afterwards, we obtain some formulas characterizing the geodesics with respect to the metric on the second tangent bundle. Finally, we present the harmonicity conditions for some maps.