Hamiltonian quaternionic transverse tangent

Proved

BirkhoffGlobalSection.hamiltonian_quaternionic_transverse_tangent

by Mazecto · Oct 3, 2026 · Mathlib 0df444a (Lean v4.33.1)

differential-geometryreal-analysis

The quaternionic transverse vectors of a Hamiltonian gradient lie in the Hamiltonian differential kernel.

All displayed regularity, tangency, normalization and supplied-data hypotheses of the exact formal statement are retained.

Preamble

import Theorems.Thm_BirkhoffGlobalSection_transverse_contact_frame_bundle
open BirkhoffGlobalSection Set Filter SignType
open scoped ContDiff Topology
set_option linter.unusedVariables false


set_option autoImplicit false
set_option maxHeartbeats 800000

Formal statement

theorem BirkhoffGlobalSection.hamiltonian_quaternionic_transverse_tangent :
∀ (F : Phase → ℝ) (y : Phase),
    fderiv ℝ F y (TangentialHessian.frame (TangentialHessian.grad F y) 1) = 0 ∧
    fderiv ℝ F y (TangentialHessian.frame (TangentialHessian.grad F y) 2) = 0 := by sorry

Source

Independent extraction of component 2 of the Proved theorem BirkhoffGlobalSection.transverse_contact_frame_bundle. Original verified source: Solutions/Sol_BirkhoffGlobalSection_transverse_contact_frame_bundle.lean. Exact original component retained.

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