Applications of the Tachibana operator on problems of lifts (Q2703131)

The purpose of the present paper is, using the Tachibana operator, to study complete lifts of affinor structures along a pure cross-section of the tensor bundle and to investigate their transfers. The results obtained are to some extent similar to results previously established for tangent (cotangent) bundles in [\textit{A. Magden}, \textit{M. Kamali} and \textit{A. A. Salimov}, Turk. J. Math. 22, No. 1, 109-117 (1998; Zbl 0933.53010)]. However, there are various important differences and it appears that the problem of lifting affinor structures to the tensor bundle on the pure cross-section presents difficulties which are not encountered in the case of the tangent (cotangent) bundle.