AN EXPLICIT FORMULA FOR THE LEVI FORM OF THE DISTANCE FUNCTION TO REAL HYPERSURFACES IN Cⁿ

Abstract

For a real hypersurface M of class C² in Cⁿ , n ≥ 2, an explicit formula for the Levi form of the distance function δ_M to M is given in terms of the Hermitian matrix (∂²ρ/∂zi∂zj) and the symmetric matrix (∂²ρ/∂zi∂zj) determined by the defining function ρ with || grad ρ || = 1 of M.