#19147: Affine connections on smooth manifolds
-------------------------------------+-------------------------------------
Reporter: egourgoulhon | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.10
Component: geometry | Resolution:
Keywords: differentiable | Merged in:
manifold, affine connection, | Reviewers:
curvature, torsion | Work issues:
Authors: Eric Gourgoulhon, | Commit:
Michal Bjeger, Marco Mancini | 0032d27fc5cbcf9c33dc681c19a5f09ac7491354
Report Upstream: N/A | Stopgaps:
Branch: |
public/manifolds/diff_manif_connections|
Dependencies: #18100, #19092 |
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Description changed by egourgoulhon:
Old description:
> 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
> `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
>
> '''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].
New description:
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].
--
--
Ticket URL: <http://trac.sagemath.org/ticket/19147#comment:9>
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