On the Integrability Conditions and Operators of the F((K + 1) (K − 1))− Structure Satisfying F K+1 + F K−1 = 0, (F 6= 0, K 1 2) on Cotangent Bundle and Tangent Bundle

Authors : Lovejoy DAS, Haşim ÇAYIR

Pages : 94-106

Doi:10.36890/iejg.559746

View : 41 | Download : 8

Publication Date : 2020-01-30

Article Type : Research Paper

Abstract :This paper consists of two main sections. In the first part, we find the integrability conditions of the horizontal lifts of $Finsert ignore into journalissuearticles values(insert ignore into journalissuearticles values(K+1); insert ignore into journalissuearticles values(K-1););-$ structure satisfying $F^{K+1}+F^{K-1}=0,$ $insert ignore into journalissuearticles values(F\neq 0,$ $K\eqslantgtr 2);$. Later, we get the results of Tachibana operators applied to vector and covector fields according to the horizontal lifts of $Finsert ignore into journalissuearticles values(insert ignore into journalissuearticles values(K+1); insert ignore into journalissuearticles values(K-1););-$structure in cotangent bundle $T^{\ast }insert ignore into journalissuearticles values(M^{n});$. Finally, we have studied the purity conditions of Sasakian metric with respect to the horizontal lifts of the structure. In the second part, all results obtained in the first section were obtained according to the complete and horizontal lifts of the structure in tangent bundle $Tinsert ignore into journalissuearticles values(M^{n});$.
Keywords : Integrability conditions, Tachibana operators, CR Submanifolds, CR Stucture, tangent bundle, cotangent bundle

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