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:
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 egourgoulhon)

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 git

  • Commit changed from 0e013aee30e3cfc05918943aa419a3d2336c01ec to 477d0577753ca790205ea115053aefad1fed0d0c

Branch pushed to git repo; I updated commit sha1. New commits:

477d057Add doctests to AffineConnection; full coverage

comment:2 Changed 4 years ago by egourgoulhon

  • Description modified (diff)
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