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

Year 2021, Volume: 9 Issue: 2, 281 - 291, 15.10.2021

Haşim Çayır

Abstract

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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