On the Lifts of $F^{K}+F=0,$ $(F\neq 0,K\geqslant 0)-$Structure on Cotangent and Tangent Bundle

This paper consists of two main sections. In the first part, we find the integrability conditions by calculating Nijenhuis tensors of the horizontal lifts of $F(K,1)-$structure satisfying $F^{K}+F=0$. Later, we get the results of Tachibana operators applied to vector and covector fields according to the horizontal lifts of $F(K,1)-$structure in cotangent bundle $ T^{\ast }(M^{n})$. Finally, we have studied the purity conditions of Sasakian metric with respect to the horizontal lifts of $F(K,1)-$structure. In the second part, all results obtained in the first section were obtained according to the complete and horizontal lifts of $F(K,1)-$structure in tangent bundle $T(M^{n})$.

Keywords:

Integrability conditions, Tachibana operators, lifts, Sasakian metric, tangent bundle cotangent bundle,

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Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: Mehmet Zeki SARIKAYA

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