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

Second Fundamental Form QF

defprovedFoundations

Documentation

Lean 4 Proof

def secondFundamentalFormQF (J : ℕ) (ρ c : ℝ) (v : Fin J → ℝ) : ℝ :=
  cesPrincipalCurvature J ρ c * vecNormSq J v

Dependency Graph

Used by

isoquant_umbilic secondFF_from_hessian

Location

thesis/CESProofs/Foundations/IsoquantGeometry.lean:68

Module Section

Differential Geometry of CES Isoquants (Gap #6)

In the same file

gradientNormSq unitNormalComponent gradientNormSq_pos tangentSpace_is_onePerp induced_metric_eq_vecNormSq 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 spaceForm_at_symmetry intrinsic_always_nonneg