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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.

MSC:

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
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