#19209: Pseudo-Riemannian metrics on smooth manifolds
-------------------------------------+-------------------------------------
Reporter: egourgoulhon | Owner: egourgoulhon
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.10
Component: geometry | Resolution:
Keywords: differentiable | Merged in:
manifold, pseudo-Riemannian | Reviewers:
metric, Riemannian metric, | Work issues:
Lorentzian metric, Levi-Civita | Commit:
connection | 0cf017a834aba4dffed1ba76eaa72ebef723471a
Authors: Eric Gourgoulhon, | Stopgaps:
Michal Bjeger, Marco Mancini |
Report Upstream: N/A |
Branch: |
public/manifolds/diff_manif_metrics|
Dependencies: #18100, #19147 |
-------------------------------------+-------------------------------------
Changes (by egourgoulhon):
* status: new => needs_review
* milestone: sage-6.9 => sage-6.10
Old description:
> This ticket implements pseudo-riemannian metrics on infinitely
> differentiable manifolds (i.e. smooth manifolds) over '''R'''. This is a
> follow-up of #19147 within the [http://sagemanifolds.obspm.fr/
> SageManifolds project] (see the metaticket #18528 for an overview).
>
> This ticket implements the following Python classes:
>
> - `PseudoRiemannianMetric` for pseudo-Riemannian metrics on a real smooth
> manifold
> - `PseudoRiemannianMetricParal` for pseudo-Riemannian metrics on a real
> smooth parallelizable manifold
> - `LeviCivitaConnection` for the Levi-Civita connection associated with a
> pseudo-Riemannian metric.
>
> Various methods of the above classes allow for the computation of
>
> - the connection coefficients and Christoffel symbols of the Levi-Civita
> connection associated with a
> given metric
> - the Riemann and Ricci tensor of a given metric
> - the Ricci scalar of a given metric
> - the Weyl tensor of a given metric
> - the volume n-form associated with a given metric on a n-dimensional
> manifold
> - the metric duals of tensor fields (musical isomorphisms)
>
> The user interface is via the method `DiffManifold.metric()`. At the user
> choice, CPU-demanding computations (like that of the Riemann tensor) can
> be parallelized, thanks to #18100.
New description:
This ticket implements pseudo-riemannian metrics on infinitely
differentiable manifolds (i.e. smooth manifolds) over '''R'''. This is a
follow-up of #19147 within the [http://sagemanifolds.obspm.fr/
SageManifolds project] (see the metaticket #18528 for an overview).
This ticket implements the following Python classes:
- `PseudoRiemannianMetric` for pseudo-Riemannian metrics on a real smooth
manifold
- `PseudoRiemannianMetricParal` for pseudo-Riemannian metrics on a real
smooth parallelizable manifold
- `LeviCivitaConnection` for the Levi-Civita connection associated with a
pseudo-Riemannian metric.
Various methods of the above classes allow for the computation of
- the connection coefficients and Christoffel symbols of the Levi-Civita
connection associated with a
given metric
- the Riemann and Ricci tensor of a given metric
- the Ricci scalar of a given metric
- the Weyl tensor of a given metric
- the volume n-form associated with a given metric on a n-dimensional
manifold
- the metric duals of tensor fields (musical isomorphisms)
The user interface is via the method `DiffManifold.metric()`. At the user
choice, CPU-demanding computations (like that of the Riemann tensor) can
be parallelized, thanks to #18100.
'''Documentation''':
The reference manual is produced by
`sage -docbuild reference/manifolds html`
It can also be accessed online at
http://sagemanifolds.obspm.fr/doc/19209/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/19209#comment:16>
Sage <http://www.sagemath.org>
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