feat: Exponential map of Lie group is smooth

[idontgetoutmuch]

We construct the exponential map expLie : g → G for a Lie group G and prove that it
is smooth. The main reference is:

• Eckhard Meinrenken, Lie Groups and Lie Algebras, Lecture Notes, University of Toronto.
  Available at https://www.math.toronto.edu/mein/teaching/LectureNotes/lie.pdf

---

[github-actions]

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[github-actions]

✅ PR Title Formatted Correctly

The title of this PR has been updated to match our commit style conventions.
Thank you!

[wwylele]

It looks like you committed some unrelated files. Could you clean them up?

[github-actions]

PR summary b43655dfe2

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Geometry.Manifold.Algebra.SmoothLieExp (new file)	2823

---

Declarations diff

+ IsMIntegralCurve.exists_global
+ IsMIntegralCurve.left_translate
+ IsMIntegralCurve.time_shift
+ IsMIntegralCurve.unique_global
+ IsMIntegralCurveOn.left_translate
+ contMDiff_dMult
+ contMDiff_dMultProd
+ contMDiff_expLie
+ contMDiff_mulLeft_deriv
+ contMDiff_zeroSectionProdFiber
+ dMult
+ dMultProd
+ dMultProd_zeroSectionProdFiber_eq
+ expLie
+ expLie_smul
+ expLie_zero
+ isMIntegralCurve_expLie_smul
+ isMIntegralCurve_prod_mk
+ mfderiv_mul_apply_zero_right
+ smooth_augmentedVF
+ smooth_tangentBundle_mk
+ zeroSectionProdFiber

You can run this locally as follows

## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>

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

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

---

No changes to technical debt.

You can run this locally as

./scripts/reporting/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).