Complex extensions of semisimple symmetric spaces
Laura Geatti
Abstract
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 GC/HC to define a G-invariant pseudo-Kaehler metric on distinguished G-invariant domains in GC/HC or on coverings of principal orbit strata in GC/HC.
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