Opened 12 months ago

Last modified 2 months ago

#30781 new enhancement

Covariant Derivatives along smooth Maps

Reported by: gh-mjungmath Owned by:
Priority: major Milestone: sage-9.5
Component: manifolds Keywords:
Cc: egourgoulhon, tscrim Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description (last modified by gh-mjungmath)

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 (4)

comment:1 Changed 12 months ago by gh-mjungmath

  • Description modified (diff)

comment:2 Changed 12 months ago by mkoeppe

  • Milestone changed from sage-9.2 to sage-9.3

comment:3 Changed 8 months ago by mkoeppe

  • Milestone changed from sage-9.3 to sage-9.4

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

comment:4 Changed 2 months ago by mkoeppe

  • Milestone changed from sage-9.4 to sage-9.5
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