#19209 closed enhancement (fixed)
PseudoRiemannian metrics on smooth manifolds
Reported by:  egourgoulhon  Owned by:  egourgoulhon 

Priority:  major  Milestone:  sage7.5 
Component:  geometry  Keywords:  differentiable manifold, pseudoRiemannian metric, Riemannian metric, Lorentzian metric, LeviCivita connection 
Cc:  mbejger, mmancini  Merged in:  
Authors:  Eric Gourgoulhon, Michal Bejger, Marco Mancini  Reviewers:  Volker Braun 
Report Upstream:  N/A  Work issues:  
Branch:  c622eb9 (Commits, GitHub, GitLab)  Commit:  
Dependencies:  #18100, #19147  Stopgaps: 
Description (last modified by )
This ticket implements pseudoriemannian metrics on infinitely differentiable manifolds (i.e. smooth manifolds) over R. This is a followup of #19147 within the SageManifolds project (see the metaticket #18528 for an overview).
This ticket implements the following Python classes:
PseudoRiemannianMetric
for pseudoRiemannian metrics on a real smooth manifoldPseudoRiemannianMetricParal
for pseudoRiemannian metrics on a real smooth parallelizable manifold
LeviCivitaConnection
for the LeviCivita connection associated with a pseudoRiemannian metric.
Various methods of the above classes allow for the computation of
 the connection coefficients and Christoffel symbols of the LeviCivita connection associated with a given metric
 the Riemann and Ricci tensor of a given metric
 the Ricci scalar of a given metric
 the Weyl tensor of a given metric
 the volume nform associated with a given metric on a ndimensional manifold
 the metric duals of tensor fields (musical isomorphisms)
The user interface is via the method DifferentiableManifold.metric()
. At the user choice, CPUdemanding computations (like that of the Riemann tensor) can be parallelized, thanks to #18100.
Documentation:
The reference manual is produced by
sage docbuild reference/manifolds html
It can also be accessed online at http://sagemanifolds.obspm.fr/doc/19209/reference/manifolds/
More documentation (e.g. example worksheets) can be found here.
Change History (38)
comment:1 Changed 6 years ago by
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comment:2 Changed 6 years ago by
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1778a4c  Add method hodge_dual() in classes DiffForm, DiffFormParal and DiffScalarField

comment:3 Changed 6 years ago by
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a6ed45c  Full doctest coverage of pseudoRiemannian metrics

comment:4 Changed 6 years ago by
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a128877  Full doctest coverage for LeviCivita connections

comment:5 Changed 6 years ago by
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03143c5  Various improvements, in particular in method open_subset() of Top/DiffManifold

comment:6 Changed 6 years ago by
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3c5fc6f  Many improvements in the documentation of topological manifolds.

comment:7 Changed 6 years ago by
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7240be3  Many improvements in the doc of top and diff manifolds

comment:8 Changed 6 years ago by
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045e736  Add global function xder + deprecated functions (Manifold, diff_mapping, function_chart)

comment:9 Changed 6 years ago by
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60a4edd  Add pushforward to differentiable maps

comment:10 Changed 6 years ago by
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8ecc57a  Minor changes in differentiable manifolds.

comment:11 Changed 6 years ago by
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5b3a961  Introduce open covers on topological manifolds and change TensorField.__eq__

comment:12 Changed 6 years ago by
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433f93f  Minor improvements in documentation of algebras of scalar fields and diff. manifolds

comment:13 Changed 6 years ago by
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889555e  Very minor changes in manifold.py and chart.py

comment:14 Changed 6 years ago by
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6ecd5db  Improve TensorField.__eq__ (case with no open cover known)

comment:15 Changed 6 years ago by
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Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
a6d4bd4  Merge branch 'public/18100parallelization_tensors' into Sage 6.7

81f662c  Improve documentation of class TensorParallelCompute.

ea38c84  In doc, changed processor with process

819661d  Changed variables name : set_nproc to set_nproc_tensor, get_nproc to get_nproc_tensor

53c248c  Parallelization: corrected doc

0bb79a3  Merge #18100 into #19124

a148062  Major improvements in the documentation of diff. manifolds (affine connections part)

a80dccc  Improve TensorField.__eq__ (case with no open cover known)

f86e5db  Merge #19147 into (#19124 + #18100)

0cf017a  Merge #19209 into #19147

comment:16 Changed 6 years ago by
 Description modified (diff)
 Milestone changed from sage6.9 to sage6.10
 Status changed from new to needs_review
comment:17 Changed 6 years ago by
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Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
2605c0b  Merge #18529 (Topological manifolds: basics) into #18175 (Implement categories for topological...)

6dec6d5  Implement topological manifolds (basics, #18529) on the new categories for manifolds (#18175)

3403978  Implement top. manifolds (scalar fields, #18640) on the new manifold categories (#18175)

b0521ef  Implement top. manifolds (morphisms, #18725) on the new manifold categories (#18175)

f643097  Implement diff. manifolds (basics, #18783) on the new manifold categories (#18175)

a527726  Implement diff. manifolds (tensor fields, #18843) on the new manifold categories (#18175)

22923ab  Implement diff. manifolds (tangent spaces, #19092) on the new manifold categories (#18175).

666bbab  Implement diff. manifolds (curves, #19124) on the new manifold categories (#18175)

fea227e  Implement diff. manifolds (affine connections, #19147) on the new manifold categories (#18175).

82f6f49  Implement diff. manifolds (metrics, #19209) on the new manifold categories (#18175).

comment:18 Changed 6 years ago by
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Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
e8f11ff  Fix pickling test in tensor field modules.

a967787  Suppress direct call to _element_constructor_ in tensor field parent classes

1bf77fd  Tangent spaces on differentiable manifolds without unique representation

dca7f9d  Curves on differentiable manifolds without unique representation

bcd87e3  Merge branch 'public/manifolds/diff_manif_curves' of git://trac.sagemath.org/sage into diff_manif_connections

0032d27  Affine connections on differentiable manifolds without unique representation

8be9a45  Merge branch 'public/manifolds/diff_manif_metrics' of git://trac.sagemath.org/sage into #19147 (affine connections on manifolds with unique representation).

8f0659a  PseudoRiemannian metrics on smooth manifolds without unique representation

1344776  Add method AffineConnection.__ne__

cb47399  Merge branch 'diff_manif_connections' into diff_manif_metrics to propagate minor changes in affine connections.

comment:19 Changed 6 years ago by
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d3e5d4d  Revert to UniqueRepresentation for topological manifolds

2481359  Revert to UniqueRepresentation for ScalarFieldAlgebra; better ScalarField constructor

0cc06e8  Revert to UniqueRepresentation for topological manifold homsets

322d5bd  Revert to UniqueRepresentation for differentiable manifolds

45beae5  Revert to UniqueRepresentation for differentiable manifolds: tensor fields

98c6036  Revert to UniqueRepresentation for differentiable manifolds: tangent spaces

b836212  Revert to UniqueRepresentation for differentiable manifolds: curves

26e8dae  First argument of scalar field constructor is the scalar field algebra (i.e. the parent)

0ea8b0c  Revert to UniqueRepresentation for differentiable manifolds: affine connections

58723e9  Revert to UniqueRepresentation for differentiable manifolds: metric

comment:20 Changed 6 years ago by
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Branch pushed to git repo; I updated commit sha1. New commits:
85d03dc  Change the argument type to structure in Manifold

5251ef0  Remove method _test_pickling from class TopologicalManifoldPoint

f69c9ee  Fix doctest error in coord_func_symb.py due to #19312 (update to pynac0.5.2)

7889a5d  Change in simplify_sqrt_real to cope with the change of != operator induced by #19312 (Sage 6.10.beta7)

e8d2ba6  Differentiable manifolds: basics with the change in symbolic expression logic induced by #19312 (Sage 6.10.beta7)

0d68f86  Diff. manifolds: tensor fields, with the change in symbolic expression logic induced by #19312 (Sage 6.10.beta7)

347a9cc  Diff. manifolds: tangent spaces, with the change in symbolic expression logic induced by #19312 (Sage 6.10.beta7)

6b51926  Diff. manifolds: curves, with the change in symbolic expression logic induced by #19312 (Sage 6.10.beta7)

d528d98  Diff. manifolds: affine connections, with the change in symbolic expression logic induced by #19312 (Sage 6.10.beta7)

2918953  Diff. manifolds: metrics, with the change in symbolic expression logic induced by #19312 (Sage 6.10.beta7)

comment:21 Changed 6 years ago by
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comment:22 Changed 6 years ago by
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comment:23 Changed 6 years ago by
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Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
984c3c2  Revert to simple hierarchy for manifold classes

c01048f  Scalar fields with the simplified hierarchy for manifold classes

c866d6c  Morphisms of topological manifolds with the simplified hierarchy for manifold classes

0e04631  Basics of diff. manifolds with the simplified hierarchy for manifold classes

1f226bd  Tensor fields with the simplified hierarchy for manifold classes

9fa77c4  Tangent spaces with the simplified hierarchy for manifold classes

db58a0c  Curves in diff. manifolds with the simplified hierarchy for manifold classes

0eb9d00  Added parallelization to CompFullyAntiSym.__add__

eb0d8b5  Affine connections with the simplified hierarchy for manifold classes

fb043ff  Metrics on diff. manifolds with the simplified hierarchy for manifold classes

comment:24 Changed 6 years ago by
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comment:25 Changed 6 years ago by
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Branch pushed to git repo; I updated commit sha1. New commits:
8e17d54  Merge into the latest version of #18529; improve treatment of composite functions in ExpressionNice

f00be00  Topological manifold morphisms: solved merge conflict with Sage 7.1.beta1

21b3968  Basics of diff. manifolds: solve merge conflict with Sage 7.1.beta1

8ba4b91  Tensor fields: solve merge conflict with Sage 7.1.beta1

2fad9db  Correct doctest in class DiffFormParal

b47f55f  Tangent spaces: solve merge conflict with Sage 7.1.beta1

9a74549  Curves in diff. manifolds: solve merge conflict with Sage 7.1.beta1

ba8ca47  Affine connections: solve merge conflict with Sage 7.1.beta1

7c39bbb  Metrics on diff. manifolds: solve merge conflict with Sage 7.1.beta1

comment:26 Changed 5 years ago by
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Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
9ec7d3e  Python 3 format for print in manifolds

d190b37  Morphisms of topological manifolds with coordinate functions as algebra elements

2577fc5  Fixing a (essentially trivial) doctest failure.

7125e29  Python3 format for print in morphims of topological manifolds

bd2f35a  Diff. manifolds with coordinate functions as algebra elements

73b4a03  Tensor fields with with coordinate functions as algebra elements

37521ae  Tangent spaces with coordinate functions as algebra elements

bdb91df  Curves in diff. manifolds with coordinate functions as algebra elements

0250072  Affine connections with coordinate functions as algebra elements

f527408  PseudoRiemannian metrics with coordinate functions as algebra elements

comment:27 Changed 5 years ago by
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comment:28 Changed 5 years ago by
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Branch pushed to git repo; I updated commit sha1. New commits:
4fad094  Merge branch 'public/manifolds/top_manif_morphisms' of trac.sagemath.org:sage into public/manifolds/top_manif_morphisms

cfecb18  Reviewer changes and tweaks for continuous maps ticket.

efcb618  Modify authorship for continuous maps.

84051b0  Merge branch 'public/manifolds/diff_manif_basics' of trac.sagemath.org:sage into public/manifolds/diff_manif_basics

97172dd  Basics of differentiable manifolds with changes in morphisms of topological manifolds

29832ec  Use @cached_method for VectorFieldModule.identity_map() and AutomorphismFieldGroup.one()

159afb4  Tangent spaces upon latest version of tensor fields

1b79561  Update of OpenInterval._Hom_

aa552cb  Affine connections on the latest #19124

a34b35d  PseudoRiemannian metrics on the latest #19147

comment:29 Changed 5 years ago by
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dcb08fc  Decrease doctest times in tensor fields; remove xder from the global namespace

3b1b794  Fix doctests in tangent spaces after the merge of #20770 in sage 7.3.beta3

c70792e  Update tangent spaces to the latest version of #18843 (vector fields)

0d6f47e  Merge branch 'public/manifolds/diff_manif_tangent_spaces' of trac.sagemath.org:sage into public/manifolds/lie_algebras20771

96f09ab  Added information about the vector field module being a Lie algebroid.

72396dd  Merge with latest #19092 to fix doctests after the merge of #20770 in sage 7.3.beta3

835b293  Update Lie algebroids to the latest version of #18843 (vector fields)

edde604  Update curves to the latest version of #18843 (vector fields)

e8e433c  Update affine connections to the latest version of #18843 (vector fields)

61e3791  Update metrics to the latest version of vector fields (#18843)

comment:30 Changed 5 years ago by
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comment:31 Changed 5 years ago by
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Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
7cf4ff4  Merge branch 'public/manifolds/diff_manif_tensor_fields' of trac.sagemath.org:sage into public/manifolds/diff_manif_tensor_fields

58ae506  Merge branch 'public/manifolds/diff_manif_tensor_fields' of git://trac.sagemath.org/sage into Sage 7.4.beta6

8219403  Fix documentation error; change in TensorField comparison to zero

a841f79  Python 3 compatible syntax in tensor fields

5a5f400  Slight change in TensorField.__eq__ (comparison to zero)

98efa66  Update tangent spaces to the final version of the dependency ticket #18843

a5ab39a  Update Lie algebroids to the latest version of the dependency ticket #19092

cd27531  Update curves to the latest version of the dependency ticket #19092

21b468f  Update affine connections to the latest version of the dependency ticket #19092

41c027f  Update metrics to the latest version of the dependency ticket (#19147) + Py3 preparation

comment:32 Changed 5 years ago by
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Branch pushed to git repo; I updated commit sha1. New commits:
8860387  Add missing reference Lee13

fb7f4dd  Bibliographic references for tensor fields moved to the master file

8205dca  Update tangent spaces to the last change (adding a missing reference) in the dependency ticket #18843

785300b  Bibliographic references for tangent spaces moved to the master file created by #21454

6af8ad2  Bibliographic references for vector field modules as Lie algebroids moved to the master file created by #21454

cdb3f28  Bibliographic references for curves on manifolds moved to the master file created by #21454

2113197  Bibliographic references for affine connections moved to the master file created by #21454

f5dd9d5  Bibliographic references for pseudoRiemannian metrics moved to the master file created by #21454

comment:33 Changed 5 years ago by
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comment:34 Changed 5 years ago by
 Milestone changed from sage7.4 to sage7.5
comment:35 followup: ↓ 36 Changed 5 years ago by
 Reviewers set to Volker Braun
 Status changed from needs_review to positive_review
comment:36 in reply to: ↑ 35 Changed 5 years ago by
Replying to vbraun:
Thank you !
comment:37 Changed 5 years ago by
 Branch changed from public/manifolds/diff_manif_metrics to c622eb9423ddfb66baaf0cba5e85be915b9cb68a
 Resolution set to fixed
 Status changed from positive_review to closed
comment:38 Changed 4 years ago by
 Commit c622eb9423ddfb66baaf0cba5e85be915b9cb68a deleted
wrong name
Branch pushed to git repo; I updated commit sha1. New commits:
Add the Hodge star operator to pseudoRiemannian metrics