id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
19147,Affine connections on smooth manifolds,egourgoulhon,,"This ticket implements affine connections on infinitely differentiable manifolds (i.e. smooth manifolds) . This is a follow-up of #19092 within the [http://sagemanifolds.obspm.fr/ 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 `DifferentiableManifold.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
'''Documentation''':
The reference manual is produced by
`sage -docbuild reference/manifolds html`
It can also be accessed online at http://sagemanifolds.obspm.fr/doc/19147/reference/manifolds/
More documentation (e.g. example worksheets) can be found [http://sagemanifolds.obspm.fr/documentation.html here].
",enhancement,closed,major,sage-7.5,geometry,fixed,"differentiable manifold, affine connection, curvature, torsion",mbejger mmancini,,"Eric Gourgoulhon, Michal Bejger, Marco Mancini",Volker Braun,N/A,,906c0301949b0ddaa8cd915089f8dc1ab5e2eca5,906c0301949b0ddaa8cd915089f8dc1ab5e2eca5,"#18100, #19092",