Abstract
In this chapter several additional basic concepts are introduced, which will be extensively employed in what follows. It is shown that, in any differentiable manifold, there is a one-to-one relation between vector fields and families of transformations of the manifold onto itself. This relation is essential in the study of various symmetries, as shown in Chaps. 4, 6 and 8, and in the relationship of a Lie group with its Lie algebra, treated in Chap. 7.
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Torres del Castillo, G.F. (2020). Lie Derivatives. In: Differentiable Manifolds. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-45193-6_2
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DOI: https://doi.org/10.1007/978-3-030-45193-6_2
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-45192-9
Online ISBN: 978-3-030-45193-6
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