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wip: existence of Riemannian metrics#28056

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grunweg wants to merge 25 commits intoleanprover-community:masterfrom
grunweg:exists-Riemannian-metric
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wip: existence of Riemannian metrics#28056
grunweg wants to merge 25 commits intoleanprover-community:masterfrom
grunweg:exists-Riemannian-metric

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@grunweg grunweg commented Aug 6, 2025

Work in progress: will require the material of #26221 (orthonormal frames), hence first be developed there.


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@grunweg grunweg added WIP Work in progress t-differential-geometry Manifolds etc labels Aug 6, 2025
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github-actions bot commented Aug 6, 2025

PR summary cefe7b7756

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.Geometry.Manifold.ExistsRiemannianMetric2 (new file) Mathlib.Geometry.Manifold.ExistsRiemannianMetric (new file) 2419

Declarations diff

+ ContDiffVectorBundle.isContMDiffRiemannianBundle
+ IsBilinearMap
+ IsBilinearMap.pullback
+ IsBilinearMap.pullback_clm
+ IsBilinearMap.pullback_clm_apply
+ IsBilinearMap.toContinuousLinearMap
+ IsBilinearMap.toContinuousLinearMap_apply
+ IsBilinearMap.toLinearMap
+ LinearMap.BilinMap.isBilinearMap
+ LinearMap.BilinMap.pullback
+ LinearMap.BilinMap.pullback_apply_basis
+ LinearMap.BilinMap.toContinuousLinearMap
+ LinearMap.BilinMap.toContinuousLinearMap_apply
+ RMetric
+ RMetric_aux
+ RMetric_local
+ RMetric_local_pre
+ V
+ W
+ aux
+ aux_special
+ aux_tvs
+ bar
+ condition
+ contMDiffOn_localExtensionOn
+ contMDiff_localSection
+ convex_condition
+ convex_condition1
+ convex_condition2
+ convex_mapsMatchingInner
+ convex_mapsMatchingInner2
+ convex_mapsMatchingInner3
+ evalL
+ foo_aux
+ foo_aux_prop
+ hloc
+ hloc3
+ hloc_TODO
+ instance (x : B) : AddCommGroup (W E x) := by
+ instance (x : B) : IsTopologicalAddGroup (V E x) := by
+ instance (x : B) : Module ℝ (V E x) := by
+ instance (x : B) : NormedAddCommGroup (W E x) := by
+ instance (x : B) : NormedSpace ℝ (V E x) := by
+ instance : (x : B) → AddCommGroup (V E x) := by
+ instance : (x : B) → Module ℝ (V E x) := by
+ instance : (x : B) → NormedAddCommGroup (V E x) := by
+ instance : ContMDiffVectorBundle n (F →L[ℝ] F →L[ℝ] ℝ) (W E) IB := by
+ instance : ContMDiffVectorBundle n (F →L[ℝ] ℝ) (V E) IB := by
+ instance : ContMDiffVectorBundle n (ℝ →L[ℝ] ℝ) (V E) IB := by
+ instance : ContMDiffVectorBundle n (ℝ →L[ℝ] ℝ) (W E) IB := by
+ instance : FiberBundle (F →L[ℝ] F →L[ℝ] ℝ) (W E) := by
+ instance : FiberBundle (F →L[ℝ] ℝ) (V E) := by
+ instance : FiberBundle (ℝ →L[ℝ] ℝ) (V E) := by
+ instance : FiberBundle (ℝ →L[ℝ] ℝ) (W E) := by
+ instance : TopologicalSpace (TotalSpace (F →L[ℝ] F →L[ℝ] ℝ) (W E)) := by
+ instance : TopologicalSpace (TotalSpace (F →L[ℝ] ℝ) (V E)) := by
+ instance : TopologicalSpace (TotalSpace (ℝ →L[ℝ] ℝ) (V E)) := by
+ instance : TopologicalSpace (TotalSpace (ℝ →L[ℝ] ℝ) (W E)) := by
+ instance : VectorBundle ℝ (F →L[ℝ] F →L[ℝ] ℝ) (W E) := by
+ instance : VectorBundle ℝ (F →L[ℝ] ℝ) (V E) := by
+ instance : VectorBundle ℝ (ℝ →L[ℝ] ℝ) (V E) := by
+ instance : VectorBundle ℝ (ℝ →L[ℝ] ℝ) (W E) := by
+ isBilinearMap_eval
+ isBilinearMap_evalL
+ is_good_localSection
+ localExtensionOn
+ local_section_at
+ mapsMatchingInner
+ mapsMatchingInner2
+ mapsMatchingInner3
+ mynorm
+ pullback_aux
+ pullback_bifunction
+ pullback_clm
+ pullback_clm_apply
+ pullback_clm_apply_basis
+ qux
+ rMetric_contMDiff
+ rMetric_eq
++ foo
++ instance (x : B) : ContinuousAdd (V E x) := by
++ instance (x : B) : ContinuousSMul ℝ (V E x) := by
++ instance (x : B) : Module ℝ (W E x) := by
++ instance (x : B) : TopologicalSpace (W E x) := by
++ instance : (x : B) → TopologicalSpace (V E x) := by

You can run this locally as follows
## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.


Increase in tech debt: (relative, absolute) = (2.00, 0.00)
Current number Change Type
794 2 erw

Current commit 1f5636ec7c
Reference commit cefe7b7756

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@mathlib4-dependent-issues-bot mathlib4-dependent-issues-bot added the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Aug 6, 2025
@mathlib4-merge-conflict-bot mathlib4-merge-conflict-bot added the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Aug 6, 2025
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This pull request has conflicts, please merge master and resolve them.

@grunweg grunweg mentioned this pull request Aug 7, 2025
grunweg added a commit to grunweg/mathlib4 that referenced this pull request Aug 16, 2025
I wanted this lemma both while working on an early version of leanprover-community#28056
and while working on leanprover-community#23040: time to add it.
Besides, it fills a natural API gap.
grunweg added a commit to grunweg/mathlib4 that referenced this pull request Aug 16, 2025
I wanted this lemma both while working on an early version of leanprover-community#28056
and while working on leanprover-community#23040: time to add it.
Besides, it fills a natural API gap.
@mathlib4-dependent-issues-bot mathlib4-dependent-issues-bot removed the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Aug 23, 2025
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@grunweg grunweg force-pushed the exists-Riemannian-metric branch from 2030d90 to 4bdd803 Compare August 27, 2025 18:31
@github-actions github-actions bot removed the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Aug 27, 2025
@grunweg grunweg force-pushed the exists-Riemannian-metric branch from 4bdd803 to 1f5636e Compare August 27, 2025 18:32
grunweg added a commit to grunweg/mathlib4 that referenced this pull request Oct 1, 2025
I wanted this lemma both while working on an early version of leanprover-community#28056
and while working on leanprover-community#23040: time to add it.
Besides, it fills a natural API gap.
mathlib-bors bot pushed a commit that referenced this pull request Oct 2, 2025
I wanted this lemma both while working on an early version of #28056 and while working on #23040: time to add it.
Besides, it fills a natural API gap.
joelriou pushed a commit to joelriou/mathlib4 that referenced this pull request Oct 2, 2025
I wanted this lemma both while working on an early version of leanprover-community#28056 and while working on leanprover-community#23040: time to add it.
Besides, it fills a natural API gap.
mitchell-horner pushed a commit to mitchell-horner/mathlib4 that referenced this pull request Oct 6, 2025
I wanted this lemma both while working on an early version of leanprover-community#28056 and while working on leanprover-community#23040: time to add it.
Besides, it fills a natural API gap.
BeibeiX0 pushed a commit to BeibeiX0/mathlib4 that referenced this pull request Nov 7, 2025
I wanted this lemma both while working on an early version of leanprover-community#28056 and while working on leanprover-community#23040: time to add it.
Besides, it fills a natural API gap.
@mathlib4-merge-conflict-bot mathlib4-merge-conflict-bot added the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Nov 19, 2025
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This pull request has conflicts, please merge master and resolve them.

@grunweg
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grunweg commented Feb 19, 2026

Let's close this PR in favour of #33714.

@grunweg grunweg closed this Feb 19, 2026
@grunweg grunweg deleted the exists-Riemannian-metric branch February 19, 2026 14:43
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3 participants