Complex extensions of semisimple symmetric spaces

Details Complex extensions of semisimple symmetric spaces Complex extensions of semisimple symmetric spaces

2006-03-03

arxiv.org/abs/math/0603105v1

Mathematics

Complex Variables

20 pages, to appear on Manuscr. Math. 2006

Scientific paper

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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