Opened 7 years ago

Last modified 6 years ago

#18843 closed enhancement

Differentiable manifolds: vector fields and tensor fields — at Initial Version

Reported by: egourgoulhon Owned by: egourgoulhon
Priority: major Milestone: sage-7.4
Component: geometry Keywords: differentiable manifold, tensor field, vector field, differential form
Cc: mbejger, bpillet, bpage Merged in:
Authors: Eric Gourgoulhon, Michal Bejger Reviewers:
Report Upstream: N/A Work issues:
Branch: public/manifolds/diff_manif_tensor_fields Commit: d48210c11f38f90ce656f0fa25ec550d147a1892
Dependencies: #15916, #18100, #18783 Stopgaps:

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Description

This ticket implements tensor fields (among which vector fields and differential forms) on differentiable manifolds. This is a follow-up of #18783 within the SageManifolds project (see the metaticket #18528 for an overview). As in #18783, the topological field K over which the differentiable manifold is defined is generic (with sufficient structure to define differentiability, e.g. a complete metric field), although in most applications, K=R or K=C.

This ticket implements the following Python classes:

1/ Parent classes:

  • VectorFieldModule: module of vector fields on a differentiable manifold
  • VectorFieldFreeModule: free module of vector fields on a parallelizable differentiable manifold
  • TensorFieldModule: module of tensor fields of a given type (k,l) on a differentiable manifold
  • TensorFieldFreeModule: free module of tensor fields of a given type (k,l) on a parallelizable differentiable manifold
  • DiffFormModule: module of differential forms of a given degree p (p-forms) on a differentiable manifold
  • DiffFormFreeModule: free module of differential forms of a given degree p (p-forms) on a parallelizable differentiable manifold
  • AutomorphismFieldGroup: general linear group of the module of vector fields on a differentiable manifold
  • AutomorphismFieldParalGroup: general linear group of the free module of vector fields on a parallelizable differentiable manifold

2/ Element classes:

  • TensorField: tensor field on a differentiable manifold
    • VectorField: vector field on a differentiable manifold
    • DiffForm: p-form on differentiable manifold
    • AutomorphismField: field of tangent-space automorphisms on a differentiable manifold
  • TensorFieldParal: tensor field on a parallelizable differentiable manifold
    • VectorFieldParal: vector field on a parallelizable differentiable manifold
    • DiffFormParal: p-form on parallelizable differentiable manifold
    • AutomorphismFieldParal: field of tangent-space automorphisms on a parallelizable differentiable manifold

3/ Other classes:

  • VectorFrame: vector frame on a differentiable manifold
    • CoordFrame: coordinate vector frame on a differentiable manifold
  • CoFrame: coframe (frame of 1-forms) on a differentiable manifold
    • CoordCoFrame: coordinate coframe on a differentiable manifold

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