Abstract
In this chapter several additional useful concepts are introduced, which will be extensively employed in the second half of this book. It is shown that there is a one-to-one relation between vector fields on a manifold 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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References
Hydon, P.E. (2000). Symmetry Methods for Differential Equations (Cambridge University Press, Cambridge).
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Torres del Castillo, G.F. (2012). Lie Derivatives. In: Differentiable Manifolds. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8271-2_2
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DOI: https://doi.org/10.1007/978-0-8176-8271-2_2
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-8270-5
Online ISBN: 978-0-8176-8271-2
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