Abstract
We have remarked (VII.5.02) that any vector in TM can arise as a tangent vector to a curve. It can moreover be defined in this way; Exercises 1–3 outline this construction of the tangent bundle. This way of looking at tangent vectors is central to the notation and thinking of this chapter, so if you do not do these exercises in full, at least be sure you are clear what is asserted in them. The tangent bundle is like compactness: not to be grokked in fullness from any one point of view.
“Whither the spirit was to go, they went; and they turned not as they went.”
Ezekiel 1.12
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Dodson, C.T.J., Poston, T. (1991). Connections and Covariant Differentiation. In: Tensor Geometry. Graduate Texts in Mathematics, vol 130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10514-2_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-10514-2_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-13117-6
Online ISBN: 978-3-642-10514-2
eBook Packages: Springer Book Archive