Sections / Section 5: General Hessian and Isoquant Geometry / spaceForm_at_symmetry

Space Form At Symmetry

theoremprovedFoundations

Documentation

Lean 4 Proof

theorem spaceForm_at_symmetry (J : ℕ) (ρ c : ℝ) :
    sectionalCurvature J ρ c = cesPrincipalCurvature J ρ c ^ 2 := rfl

Dependency Graph

Location

thesis/CESProofs/Foundations/IsoquantGeometry.lean:214

Module Section

Differential Geometry of CES Isoquants (Gap #6)

In the same file

gradientNormSq unitNormalComponent gradientNormSq_pos tangentSpace_is_onePerp induced_metric_eq_vecNormSq secondFundamentalFormQF gaussCurvature meanCurvatureTrace curvature_eq_neg_eigenvalue_sqrt secondFF_from_hessian gaussCurvature_pos meanCurvature_pos sectionalCurvature sectionalCurvature_nonneg sectionalCurvature_eq_zero_iff sectionalCurvature_explicit sectionalCurvature_from_K principalCurvature_trichotomy isoquant_umbilic intrinsic_always_nonneg