Opened 22 months ago
Last modified 4 months ago
#30781 new enhancement
Covariant Derivatives along smooth Maps
Reported by: | gh-mjungmath | Owned by: | |
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Priority: | major | Milestone: | sage-9.7 |
Component: | manifolds | Keywords: | |
Cc: | egourgoulhon, tscrim | Merged in: | |
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
In 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.
Since 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.
Change History (6)
comment:1 Changed 22 months ago by
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