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 $t^{\ast }M$.

Keywords

• Semi-tensor bundle,complete lift,musical isomorphism,vector field,pull-back bundle

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