Complete lifts of derivations to tensor bundles. (English) Zbl 1020.53006

The authors study the complete lifts of derivations on an \(n\)-dimensional differentiable manifold \(M\) of class \(C^\infty\), and consider some geometric applications of the tangent bundle. Contents include: an introduction; vertical lifts of tensor fields and the \(\gamma\)-operator; complete lifts of derivations and \(\gamma\)-operator; complete lifts of Lie derivations; complete lifts of covariant derivations; and complete lifts of derivations determined by the curvature operator.


53A45 Differential geometric aspects in vector and tensor analysis
53B05 Linear and affine connections
55R10 Fiber bundles in algebraic topology
57R25 Vector fields, frame fields in differential topology