Opened 4 years ago
Last modified 3 years ago
#19147 closed enhancement
Affine connections on smooth manifolds — at Version 2
Reported by: | egourgoulhon | Owned by: | |
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Priority: | major | Milestone: | sage-7.5 |
Component: | geometry | Keywords: | differentiable manifold, affine connection, curvature, torsion |
Cc: | mbejger, mmancini | Merged in: | |
Authors: | Eric Gourgoulhon, Michal Bjeger, Marco Mancini | Reviewers: | |
Report Upstream: | N/A | Work issues: | |
Branch: | public/manifolds/diff_manif_connections | Commit: | 477d0577753ca790205ea115053aefad1fed0d0c |
Dependencies: | #18100, #19092 | Stopgaps: |
Description (last modified by )
This ticket implements affine connections on infinitely differentiable manifolds (i.e. smooth manifolds) . This is a follow-up of #19092 within the SageManifolds project (see the metaticket #18528 for an overview). As in #19092, the non-discrete topological field K over which the smooth manifold is defined is generic, although in most applications, K=R or K=C.
Affine connections are implemented via the Python class AffineConnection
, the user interface being the method DiffManifold.affine_connection()
. At the user choice, CPU-demanding computations (like that of the curvature tensor) can be parallelized, thanks to #18100.
Various methods of the class AffineConnection
allow the computation of
- the connection coefficients with respect to a given vector frame (from those w.r.t. another frame)
- the connection 1-forms with respect to a given vector frame
- the torsion tensor
- the torsion 2-forms with respect to a given vector frame
- the (Riemann) curvature tensor
- the curvature 2-forms with respect to a given vector frame
- the Ricci tensor
- the action of the affine connection on any tensor field
Change History (2)
comment:1 Changed 4 years ago by
- Commit changed from 0e013aee30e3cfc05918943aa419a3d2336c01ec to 477d0577753ca790205ea115053aefad1fed0d0c
comment:2 Changed 4 years ago by
- Description modified (diff)
Branch pushed to git repo; I updated commit sha1. New commits:
Add doctests to AffineConnection; full coverage