Opened 22 months ago

Last modified 20 months ago

#24622 closed enhancement

Pseudo-Riemannian manifods — at Initial Version

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: Commit:
Dependencies: Stopgaps:

Description

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.

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