A Study on the Second Order Tangent Bundles over Bi-Kählerian Manifolds  

作　　者：Nour Elhouda DJAA Aydin GEZER Abderrahim ZAGANE 

机构地区：[1]Relizane University,Faculty of Sciences and Technology,Department of Mathematics,Algeria [2]Ataturk University,Faculty of Science,Department of Mathematics,25240,Erzurum-Turkey

出　　处：《Chinese Annals of Mathematics,Series B》2024年第5期777-804,共28页数学年刊（B辑英文版）

摘　　要：This paper aims to study the Berger type deformed Sasaki metric g_(BS)on the second order tangent bundle T^(2)M over a bi-Kählerian manifold M.The authors firstly find the Levi-Civita connection of the Berger type deformed Sasaki metric g_(BS)and calculate all forms of Riemannian curvature tensors of this metric.Also,they study geodesics on the second order tangent bundle T^(2)M and bi-unit second order tangent bundle T^(2)_(1,1)M,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 sectionσ:M→T^(2)M to be harmonic and study the harmonicity of the different canonical projections and inclusions of(T^(2)M,g_(BS)).Moreover,they search the harmonicity of the Berger type deformed Sasaki metric g_(BS)and the Sasaki metric g_(S) with respect to each other.

关 键 词：Berger type deformed Sasaki metric Bi-Kählerian structure GEODESICS Harmonicity Riemannian curvature tensor Second order tangent bundle 

分 类 号：O186.1[理学—数学]