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

Abstract

The F^{v+1}-λ²F^{v-1}=0 structure (v≥3) have been studied by Kim J. B. K75. Later, Srivastava S.K studied on the complete lifts of (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 F((v+1),λ²(v-1)) -structure and the conditions of almost holomorfic vector fields in cotangent bundle T^{∗}(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 T(Mⁿ).