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Erschienen in:
2012 | OriginalPaper | Buchkapitel
2. Lie Derivatives
verfasst von : Gerardo F. Torres del Castillo
Erschienen in: Differentiable Manifolds
Verlag: Birkhäuser Boston
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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.