半单对称空间的复扩张
Complex extensions of semisimple symmetric spaces
摘要：
设G/H是伪黎曼半单对称空间。切丛T（G/H）包含适应复结构存在的零截面的极大G-不变邻域。这样的邻域被赋予一个与G/H上的度量具有相同签名的规范G-不变伪Kaehler度量。利用T（G/H）到复化对称空间G^C/H^C的极映射，在G^C/H^C中的G-不变域上或在G^C/H ^C中的主轨道层覆盖上定义了一个G-不变的伪Kaehler度量.
英文摘要：
Let G/H be a pseudo-Riemannian semisimple symmetric space. The tangent bundle T(G/H) contains a maximal G-invariant neighbourhood of the zero section where the adapted complex structure exists. Such neighbourhood is endowed with a canonical G-invariant pseudo-Kaehler metric of the same signature as the metric on G/H. We use the polar map from T(G/H) to the complexified symmetric space G^C/H^C to define a G-invariant pseudo-Kaehler metric on distinguished G-invariant domains in G^C/H^C or on coverings of principal orbit strata in G^C/H^C.
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