Opened 22 months ago

Last modified 20 months ago

#24622 closed enhancement

Pseudo-Riemannian manifods — at Version 2

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: 06f8fd34981fb8b201134439a55ecf79f962a5c9
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 generic metric tensors are already implemented in Sage (see here), this ticket introduces

  • the parent class PseudoRiemannianManifold, as a subclass of the existing class DifferentiableManifold
  • new methods gradient and laplacian for scalar fields
  • new methods divergence, laplacian for tensor fields
  • new methods curl, dot_product, cross_product 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.

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

Change History (2)

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)
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