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| A Study on the Second Order Tangent Bundles overBi-K¨ahlerian Manifolds |
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Citation： |
Nour Elhouda DJAA,Aydin GEZER,Abderrahim ZAGANE.A Study on the Second Order Tangent Bundles overBi-K¨ahlerian Manifolds[J].Chinese Annals of Mathematics B,2024,45(5):777~804 |
| Page view： 96
Net amount： 78 |
Authors： |
Nour Elhouda DJAA; Aydin GEZER;Abderrahim ZAGANE |
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| Abstract： |
This paper aims to study the Berger type deformed Sasaki metric gBS on the
second order tangent bundle T 2M over a bi-K¨ahlerian manifold M. The authors firstly find
the Levi-Civita connection of the Berger type deformed Sasaki metric gBS and calculate
all forms of Riemannian curvature tensors of this metric. Also, they study geodesics on
the second order tangent bundle T 2M and bi-unit second order tangent bundle T12,1M,
and characterize a geodesic of the bi-unit second order tangent bundle in terms of geodesic
curvatures of its projection to the base. Finally, they present some conditions for a section
σ : M → T 2M to be harmonic and study the harmonicity of the different canonical
projections and inclusions of (T 2M, gBS). Moreover, they search the harmonicity of the
Berger type deformed Sasaki metric gBS and the Sasaki metric gS with respect to each
other. |
Keywords： |
Berger type deformed Sasaki metric, Bi-K¨ahlerian structure, Geodesics,
Harmonicity,Riemannian curvature tensor,Second order tangent bundle |
Classification： |
53C07, 53C55, 53C22 |
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