REPRESENTATION AND NON-DEGENERACY CONDITION FOR LEVI FORM OF DISTANCE TO REAL HYPERSURFACES IN C^n

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概要

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• Let M be a real hypersurface of class C^2 in C^n, n ≥ 2, and let δ_M(z) be the Euclidean distance from z ∈ C^n to M. In this paper we give an explicit representation in complex tangential direction for the Levi form of the function δ_M (or -log δM) by Hermitian and symmetric matrices determined by a local defining function of M. As its application, we also show that, if M is defined by a C^2-function ρ with dρ ≠ 0, then the function -log δ_M is strictly plurisubharmonic in complex tangential direction near M if and only if M is Levi-flat and the symmetric matrix (δ^2ρ/δz_i δz_j ) of degree n has maximal rank n - 1 on the complex tangent subspace T_z^1,0 (M) ⊂ T_z^1,0 (C^n) for each z ∈ M as a linear map. Moreover, we can get directly the well-known Levi condition as the condition in order that -log δ_M is weakly plurisubharmonic in complex tangential direction near and in one side of M.

• Faculty of Mathematics, Kyushu Universityの論文

著者

• MATSUMOTO Kazuko

  Faculty of Liberal Arts and Sciences Osaka Prefecture University

関連論文

• REPRESENTATION AND NON-DEGENERACY CONDITION FOR LEVI FORM OF DISTANCE TO REAL HYPERSURFACES IN C^n

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