Some notes on lifts of the F((υ+1),λ²(υ-1))-structure on cotangent and tangent bundle

Authors : Haşim ÇAYIR

Pages : 241-264

Doi:10.31801/cfsuasmas.712861

View : 9 | Download : 8

Publication Date : 2021-06-30

Article Type : Research Paper

Abstract :The F^{v+1}-λ²F^{v-1}=0 structure insert ignore into journalissuearticles values(v≥3); have been studied by Kim J. B. K75 . Later, Srivastava S.K studied on the complete lifts of insert ignore into journalissuearticles values(1,1); tensor field F satisfying structure F^{v+1}-λ²F^{v-1}=0 and extended in Mⁿ to cotangent bundle. This paper consists of two main sections. In the first part, we find the integrability conditions by calculating Nijenhuis tensors of the complete and horizontal lifts of F^{v+1}-λ²F^{v-1}=0. Later, we get the results of Tachibana operators applied to vector and covector fields according to the complete and horizontal lifts of Finsert ignore into journalissuearticles values(insert ignore into journalissuearticles values(v+1);,λ²insert ignore into journalissuearticles values(v-1);); -structure and the conditions of almost holomorfic vector fields in cotangent bundle T^{∗}insert ignore into journalissuearticles values(Mⁿ);. Finally, we have studied the purity conditions of Sasakian metric with respect to the lifts of F^{v+1}-λ²F^{v-1}=0-structure. In the second part, all results obtained in the first section were investigated according to the complete and horizontal lifts of the F^{v+1}-λ²F^{v-1}=0 structure in tangent bundle Tinsert ignore into journalissuearticles values(Mⁿ);.
Keywords : Integrability conditions, Tachibana Operators, Horizontal lift, Complete lift, Sasakian metric, Cotangent bundle