In the previous chapter we studied vector fields and functions on manifolds. Now these objects are generalized to tensor fields, which are sections of vector bundles built out of the tangent bundle. This study is continued in the next chapter when we discuss differential forms, which are tensors with special symmetry properties. One of the objectives of this chapter is to extend the pull-back and Lie derivative operations from functions and vector fields to tensor fields.
KeywordsVector Field Vector Bundle Tensor Field Separable Banach Space Kill Vector Field
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