| 作成者 |
|
| 本文言語 |
|
| 出版者 |
|
|
|
| 発行日 |
|
| 収録物名 |
|
| 巻 |
|
| 号 |
|
| 開始ページ |
|
| 終了ページ |
|
| 出版タイプ |
|
| アクセス権 |
|
| 関連DOI |
|
| 関連DOI |
|
|
|
| 関連URI |
|
|
|
| 関連URI |
|
| 関連HDL |
|
| 関連情報 |
|
|
|
| 概要 |
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 fo...r 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.続きを見る
|
Mendeley出力
