On almost complex structures in the cotangent bundle

Authors : Arif SALIMOV, Aydin GEZER, Seher ASLANCI

Pages : 487-492

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :E. M. Patterson and K. Yano studied vertical and complete lifts of tensor fields and connections from a manifold Mn to its cotangent bundle T\ast insert ignore into journalissuearticles values(Mn);. Afterwards, K. Yano studied the behavior on the cross-section of the lifts of tensor fields and connections on a manifold Mn to T\ast insert ignore into journalissuearticles values(Mn); and proved that when j defines an integrable almost complex structure on Mn, its complete lift C j is a complex structure. The main result of the present paper is the following theorem: Let j be an almost complex structure on a Riemannian manifold Mn. Then the complete lift C j of j, when restricted to the cross-section determined by an almost analytic 1-form w on Mn, is an almost complex structure.
Keywords : Almost complex structure, cotangent bundle, cross section, Nijenhuis tensor, analytic tensor field