A.Z. Petrov divided 4-metrics of signature 0 into 6 types, which later began to be denoted by I, D, O, II, N, III. However, in the case of (anti-)self-duality, the \(\lambda\)-matrix, on the basis of which Petrov built his classification, acquires specificity. First, the determinant of this \(\lambda\)-matrix has a root 0 of multiplicity at least 3. Second, the multiplicity of this root cannot be 5. These two circumstances lead to the fact that there are not 6, but 7 different types of metrics. A new type I\(_{0}\) appears, whose characteristic number 0 has multiplicity 4. This type does not coincide with I, since for type I the multiplicity of the root 0 is three. Examples of metrics, expressed in terms of elementary functions, of all 7 types are constructed.

AZ Petrov将签名0的4度量分为6种类型，后来开始用I，D，O，II，N，III表示。但是，在（反）自我对偶的情况下，彼得罗夫建立其分类的\（\ lambda \）-矩阵获得了特异性。首先，此\（\ lambda \）-矩阵的行列式的多重性根0至少为3。其次，该根的多重性不能为5。这两种情况导致不存在6，而是7不同类型的指标。新类型I \（_ {0} \）出现，其特征数0的多重性为4。此类型与I不一致，因为对于类型I，根0的多重性为3。构造了所有7种类型的用基本功能表示的度量示例。