Theorem of Hopf-Rinow

The theorem of Hopf-Rinow says that the following properties are equivalent:

• For any point m, the application Exponentielle of origin m is defined on TmM
• the variety (M, G) is géodésiquement complete, IE: the Géodésique S are defined on $\backslash \; mathbb\; \{R\}$.
• space M is complete for the distance riemannienne.
• the closed and limited balls are compact.

Internal bond

• Variety riemannienne

Random links:

Fourth Age | François Joseph Bosio | The Manor (the Eure) | Foreign politics of the United States of America | Lucie Durbiano | Liste_d'endroits_dans_Hertfordshire

© 2007-2008 speedlook.com; article text available under the terms of GFDL, from fr.wikipedia.org