Note on the cross-section in the semi-tensor bundle

Abstract

Using the fiber bundle M over a manifold B, we define a semi-tensor (pull-back) bundle tB of type (p,q). The complete and horizontal lift of projectable geometric objects on M to the semi-tensor (pull-back) bundle tB of type (p,q) are presented. The main purpose of this paper is to study the behaviour of complete lift of vector and affinor (tensor of type (1,1)) fields on cross-sections for pull-back (semi-tensor) bundle tB of type (p,q).