Timeline for Domain of definition of a certain mapping
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 6, 2021 at 19:05 | comment | added | Ryan Budney | This notion of distance is the one used in the "Hopf-Rinow Theorem". You compute it as the shortest-length geodesic between two points (if the manifold isn't complete you need to use infima). Most of these references suffice: mathoverflow.net/questions/19505/… In that list, my preference is the Gallot, Hulin, Lafontaine text. | |
| Nov 6, 2021 at 18:46 | comment | added | Giuseppe Tenaglia | Do you know any introductory book for differential geometry? I am extremely new to the topic | |
| Nov 6, 2021 at 18:46 | comment | added | Giuseppe Tenaglia | If I do not have a distance in the manifold, how can I consider the concept of radius? | |
| Nov 6, 2021 at 18:36 | comment | added | Ryan Budney | I suppose I view the injectivity radius as telling you the maximal radius open ball in the domain of $exp_x^{-1}$. | |
| Nov 6, 2021 at 18:32 | comment | added | Giuseppe Tenaglia | Why is knowing the injectivity radius enough? I think I also need to take into account how to deal with the domain of the inverse. In other words, I think I need also the domain of definition of $\exp_{x}^{-1}$ | |
| Nov 6, 2021 at 18:16 | comment | added | Ryan Budney | It sounds like you are interested in the radius of injectivity for the exponential map? This is a topic of many introductory differential geometry textbooks. | |
| Nov 6, 2021 at 17:38 | history | asked | Giuseppe Tenaglia | CC BY-SA 4.0 |