#19209: Pseudo-Riemannian metrics on smooth manifolds
-------------------------------------+-------------------------------------
Reporter: egourgoulhon | Owner: egourgoulhon
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.9
Component: geometry | Keywords: differentiable
Merged in: | manifold, pseudo-Riemannian metric,
Reviewers: | Riemannian metric, Lorentzian
Work issues: | metric, Levi-Civita connection
Commit: | Authors: Eric Gourgoulhon,
8304102cee532d2a6fae11cbfc4a48711de4a1ee| Michal Bjeger, Marco Mancini
Stopgaps: | Report Upstream: N/A
| Branch:
| public/manifolds/diff_manif_metrics
| Dependencies: #18100, #19147
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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.
--
Ticket URL: <http://trac.sagemath.org/ticket/19209>
Sage <http://www.sagemath.org>
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