- Differential Geometry
Clifford Henry Taubes
- Oxford University Press
Let M denote a smooth manifold. A metric on TM can be used to define a notion of the distance between any two points in M and the distance travelled along any given path in M. This chapter first explains how this is done then considers the distance minimizing paths. The discussions cover Riemannian metrics and distance; length minimizing curves; the existence of geodesics; examples of metrics with their corresponding geodesics; geodesics on SO(n); geodesics on U(n) and SU(n); and geodesics and matrix groups.
metrics, distance, Riemannian metrics, length minimizing curves, matrix groups
Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
Please, subscribe or login to access full text content.
If you think you should have access to this title, please contact your librarian.
To troubleshoot, please check our
, and if you can't find the answer there, please