On integrability conditions, operators, and the purity conditions of the Sasakian metric with respect to lifts of Fλ(7, 1)-structure on the cotangent bundle

Authors : Haşim ÇAYIR

Pages : 186-198

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :There are many structures in the cotangent bundle. These include the complete and horizontal lifts of the $F_{\lambda }insert ignore into journalissuearticles values(7,1);$-structure. The $F_{\lambda }insert ignore into journalissuearticles values(7,1);$-structure was first extended in $M^{n}$ to $T^{\ast }insert ignore into journalissuearticles values(M^{n});$ by Das, Nivas, and Pathak. Later, the horizontal and complete lift of the $F_{a}insert ignore into journalissuearticles values(K,1);$-structure in the tangent bundle was given by Prasad and Chauhan. This paper consists of two main sections. In the first part, we find the integrability conditions by calculating Nijenhuis tensors of the complete lifts of the $F_{\lambda }insert ignore into journalissuearticles values(7,1);$-structure. Later, we get the results of the Tachibana operators applied to vector and covector fields according to the complete lifts of the $% F_{\lambda }insert ignore into journalissuearticles values(7,1);$-structure in the cotangent bundle $T^{\ast }insert ignore into journalissuearticles values(M_{n});$. Finally, we study the purity conditions of the Sasakian metric with respect to the complete lifts of the $F_{\lambda }insert ignore into journalissuearticles values(7,1);$-structure. In the second part, all results obtained in the first section are obtained according to the horizontal lifts of the $F_{\lambda }insert ignore into journalissuearticles values(7,1);$-structure in cotangent bundle $T^{\ast }insert ignore into journalissuearticles values(M_{n});$.
Keywords : Integrability conditions, Tachibana operators, horizontal lift, complete lift, Sasakian metric, cotangent bundle