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.
KeywordsVector Field Tangent Vector Integral Curve Tensor Field Infinitesimal Generator
- Hydon, P.E. (2000). Symmetry Methods for Differential Equations (Cambridge University Press, Cambridge). Google Scholar