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[Merged by Bors] - feat(geometry/manifold): derivative of the zero section of the tangent bundle #4292

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sgouezel
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We show that the zero section of the tangent bundle to a smooth manifold is smooth, and compute its derivative.

Along the way, some streamlining of supporting material.

@kodyvajjha
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I'm not too familiar with this part of mathlib, and this may already exist, but does it also make sense to add similar results about tangent_bundle.proj?

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The results on smoothness of the projection are already there. For instance,

lemma smooth_proj : smooth I.tangent I (proj I M) :=
basic_smooth_bundle_core.smooth_proj _

is already in times_cont_mdiff.lean.

@robertylewis robertylewis added the awaiting-review The author would like community review of the PR label Sep 28, 2020
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This looks good to me. I have suggested some docstring changes, covering mathematical points that occurred to me as I read the file and that therefore might be useful to someone else. Feel free to accept, reject, or re-work any of them.

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sgouezel and others added 3 commits October 1, 2020 09:37
Co-authored-by: hrmacbeth <25316162+hrmacbeth@users.noreply.github.com>
Co-authored-by: hrmacbeth <25316162+hrmacbeth@users.noreply.github.com>
Co-authored-by: hrmacbeth <25316162+hrmacbeth@users.noreply.github.com>
@sgouezel
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sgouezel commented Oct 1, 2020

Thanks for your suggestions!

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Great!
bors r+

@github-actions github-actions bot added ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) and removed awaiting-review The author would like community review of the PR labels Oct 1, 2020
bors bot pushed a commit that referenced this pull request Oct 1, 2020
…t bundle (#4292)

We show that the zero section of the tangent bundle to a smooth manifold is smooth, and compute its derivative.

Along the way, some streamlining of supporting material.
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bors bot commented Oct 1, 2020

Pull request successfully merged into master.

Build succeeded:

@bors bors bot changed the title feat(geometry/manifold): derivative of the zero section of the tangent bundle [Merged by Bors] - feat(geometry/manifold): derivative of the zero section of the tangent bundle Oct 1, 2020
@bors bors bot closed this Oct 1, 2020
@bors bors bot deleted the zero_section branch October 1, 2020 16:43
adomani pushed a commit that referenced this pull request Oct 7, 2020
…t bundle (#4292)

We show that the zero section of the tangent bundle to a smooth manifold is smooth, and compute its derivative.

Along the way, some streamlining of supporting material.
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4 participants