Changes between Initial Version and Version 1 of Ticket #30781


Ignore:
Timestamp:
Oct 17, 2020, 12:24:36 PM (2 years ago)
Author:
Michael Jung
Comment:

Legend:

Unmodified
Added
Removed
Modified
  • Ticket #30781 – Description

    initial v1  
    11In the current implementation of connections, it is not possible to take the covariant derivative along a map. But this is especially useful when the maps are curves, most prominently geodesics.
    22
    3 Since this construction is simply taking the pull-back of a connection along a map in terms of bundles, I'd suggest to utilize the implementation for general vector bundles, which already support the desired action (see #30209). The covariant derivative along a curve would then correspond to the pull-back connection on the corresponding pulled-back vectorfield module. Different approaches are most welcome.
     3Since this construction is nothing but taking the pull-back of a connection along a map in terms of bundles, I'd suggest to utilize the implementation over general vector bundles, which already support the desired action (see #30209). The covariant derivative along a curve would then correspond to the pull-back connection on the corresponding pulled-back vectorfield module. Different approaches are most welcome for discussion.