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: |

### 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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