Problems of Lifts in Symplectic Geometry

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英文篇名：Problems of Lifts in Symplectic Geometry 作者：Arif ; SALIMOV ; Manouchehr ; BEHBOUDI ; ASL ; Sevil ; KAZIMOVA 英文作者：Arif SALIMOV;Manouchehr BEHBOUDI ASL;Sevil KAZIMOVA;Department of Algebra and Geometry, Baku State University;Department of Mathematics, Salmas Branch, Islamic Azad University; 英文关键词：Symplectic manifold;;Tangent bundle;;Cotangent bundle;;Transform of tensor fields;;Pullback;;Pure tensor;;Holomorphic manifold 中文刊名：SXNK 英文刊名：数学年刊B辑(英文版) 机构：Department of Algebra and Geometry, Baku State University;Department of Mathematics, Salmas Branch, Islamic Azad University; 出版日期：2019-05-15 出版单位：Chinese Annals of Mathematics,Series B 年：2019 期：v.40 语种：英文; 页：SXNK201903001 页数：10 CN：03 ISSN：31-1329/O1 分类号：5-14

摘要

Let(M,ω)be a symplectic manifold.In this paper,the authors consider the notions of musical(bemolle and diesis)isomorphisms ω~b:T M→T~*M and ω~?:T~*M→TM between tangent and cotangent bundles.The authors prove that the complete lifts of symplectic vector field to tangent and cotangent bundles is ω~b-related.As consequence of analyze of connections between the complete lift ~cω_(T M )of symplectic 2-form ω to tangent bundle and the natural symplectic 2-form dp on cotangent bundle,the authors proved that dp is a pullback o f~cω_(TM)by ω~?.Also,the authors investigate the complete lift ~cφ_T~*_M )of almost complex structure φ to cotangent bundle and prove that it is a transform by ω~?of complete lift~cφ_(T M )to tangent bundle if the triple(M,ω,φ)is an almost holomorphic A-manifold.The transform of complete lifts of vector-valued 2-form is also studied.
        Let(M,ω)be a symplectic manifold.In this paper,the authors consider the notions of musical(bemolle and diesis)isomorphisms ω~b:T M→T~*M and ω~?:T~*M→TM between tangent and cotangent bundles.The authors prove that the complete lifts of symplectic vector field to tangent and cotangent bundles is ω~b-related.As consequence of analyze of connections between the complete lift ~cω_(T M )of symplectic 2-form ω to tangent bundle and the natural symplectic 2-form dp on cotangent bundle,the authors proved that dp is a pullback o f~cω_(TM)by ω~?.Also,the authors investigate the complete lift ~cφ_T~*_M )of almost complex structure φ to cotangent bundle and prove that it is a transform byω~?of complete lift~cφ_(T M )to tangent bundle if the triple(M,ω,φ)is an almost holomorphic A-manifold.The transform of complete lifts of vector-valued 2-form is also studied.

引文

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