Opened 22 months ago

Last modified 20 months ago

#24622 closed enhancement

Pseudo-Riemannian manifods — at Version 9

Reported by: egourgoulhon Owned by:
Priority: major Milestone: sage-8.2
Component: geometry Keywords: pseudo-Riemannian, Riemannian, manifold, gradient, divergence, Laplacian
Cc: tscrim Merged in:
Authors: Eric Gourgoulhon Reviewers:
Report Upstream: N/A Work issues:
Branch: public/manifolds/pseudoRiemannian (Commits) Commit: 46b8f66385cd1c34e5310d627a0e44983f87cc4a
Dependencies: Stopgaps:

Description (last modified by egourgoulhon)

This ticket implements pseudo-Riemannian manifolds, i.e. real differentiable manifolds equipped with a metric tensor. Important subcases are of course Riemannian manifolds and Lorentzian manifolds. Taking into account that pseudo-Riemannian metric tensors are already implemented in Sage (see here), this ticket introduces

  • the parent class PseudoRiemannianManifold, as a subclass of the existing class DifferentiableManifold, with the specific methods metric and volume_form
  • new methods gradient, laplacian and dalembertian for scalar fields
  • new methods divergence, laplacian and dalembertian for tensor fields
  • new methods curl, dot, cross and norm for vector fields

For a greater generality, all these methods have an optional argument metric; if it is omitted, the metric of the underlying pseudo-Riemannian manifold is assumed. The follow-up ticket #24623 implements Euclidean spaces.

This work is part of the SageManifolds project, see #18528 for an overview.

Change History (9)

comment:1 Changed 22 months ago by egourgoulhon

  • Branch set to public/manifolds/pseudoRiemannian
  • Commit set to 06f8fd34981fb8b201134439a55ecf79f962a5c9

This is work in progress...


New commits:

8e1148cFirst version of pseudo-Riemannian manifold class
8e56cf3Pseudo-Riemannian manifolds constructed by the generic function Manifold
ce3a617Divergence of a tensor field + new section on pseudo-Riemannian manifolds in the reference manual
06f8fd3Add doctests for pseudo-Riemannian manifolds

comment:2 Changed 22 months ago by egourgoulhon

  • Description modified (diff)

comment:3 Changed 22 months ago by egourgoulhon

  • Description modified (diff)

comment:4 Changed 22 months ago by git

  • Commit changed from 06f8fd34981fb8b201134439a55ecf79f962a5c9 to 55f356c2ee79026349a821dccd409d0d5a76718c

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

55f356cImprove documentation of pseudo-Riemannian manifolds

comment:5 Changed 22 months ago by git

  • Commit changed from 55f356c2ee79026349a821dccd409d0d5a76718c to 0fc661a5beaf076fdf67e0d4f45b546ed8e23e8e

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

0fc661aRemove method set_metric and improve doc of pseudo-Riemannian manifolds

comment:6 Changed 22 months ago by git

  • Commit changed from 0fc661a5beaf076fdf67e0d4f45b546ed8e23e8e to b4dddf74279a21aa9cc645f959c8cd6b513a8d48

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

b4dddf7Add operators Laplacian, d'Alembertian and curl on pseudo-Riemannian manifolds

comment:7 Changed 22 months ago by git

  • Commit changed from b4dddf74279a21aa9cc645f959c8cd6b513a8d48 to 040b01c35f3082b4788bdeefea9d28aa1f96d3bc

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

040b01cAdd dot product and cross product of vector fields

comment:8 Changed 22 months ago by git

  • Commit changed from 040b01c35f3082b4788bdeefea9d28aa1f96d3bc to 46b8f66385cd1c34e5310d627a0e44983f87cc4a

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

46b8f66Add norm of vector fields.

comment:9 Changed 22 months ago by egourgoulhon

  • Description modified (diff)
Note: See TracTickets for help on using tickets.