Musical Isomorphisms on the Semi-Tensor Bundles

Abstract

We transfer vertical lifts and complete lifts of some tensor fields from the semi-tangent bundle $tM$ to the semi-cotangent bundle $t^{\ast }M$ \ using a musical isomorphism between these bundles. In this article, we also analyze complete lift of vector and affinor (tensor of type $(1,1)$) fields for semi-tangent (pull-back) bundle $tM$. Finally, we study compatibility of transferring lifts with complete lifts in the semi-cotangent bundle $t^{\ast }M$.