Let L be a contragredient Lie superalgebra. A symmetric pair of L is a pair \(({\mathfrak {g}},{\mathfrak {g}}^\sigma )\), where \({\mathfrak {g}}\) is a real form of L, and \(\sigma \) is a \({\mathfrak {g}}\)-involution with invariant subalgebra \({\mathfrak {g}}^\sigma \). We show that a symmetric pair carries invariant symplectic forms if and only if \({\mathfrak {g}}^\sigma \) has a 1-dimensional center. Furthermore, the symplectic form is pseudo-Kähler if and only if the center of \({\mathfrak {g}}^\sigma \) is compact. As an application, we classify the symplectic symmetric pairs, as well as the pseudo-Kähler symmetric pairs.

令L为反义李超代数。L的对称对是\（（{\ mathfrak {g}}，{\ mathfrak {g}} ^ \ sigma）\）对，其中\（{\ mathfrak {g}} \）是大号，和\（\西格玛\）是一个\（{\ mathfrak {G}} \） -involution与不变子代数\（{\ mathfrak {G}} ^ \西格玛\） 。我们证明，当且仅当\（{\ mathfrak {g}} ^ \ sigma \）具有一维中心时，对称对才具有不变的辛形式。此外，当且仅当\（{\ mathfrak {g}} ^ \ sigma \）的中心时，辛形式为伪Kähler紧凑。作为应用，我们对辛对称对以及伪Kähler对称对进行分类。