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, Volume 120, Issue 1, pp 1–25 | Cite as

Complex extensions of semisimple symmetric spaces

  • Laura GeattiEmail author


Let G/H be a pseudo-Riemannian semisimple symmetric space. The tangent bundle T(G/H) contains a maximal G-invariant neighbourhood Ω of the zero section where the adapted-complex structure exists. Such Ω is endowed with a canonical G-invariant pseudo-Kähler metric of the same signature as the metric on G/H. We use the polar map Open image in new window to define a G-invariant pseudo-Kähler metric on distinguished G-invariant domains in Open image in new window or on coverings of principal orbit strata in Open image in new window . In the rank-one case, we show that the polar map is globally injective and the domain Open image in new window is an increasing union of q-complete domains.


Number Theory Symmetric Space Algebraic Geometry Topological Group Tangent Bundle 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di Roma 2RomaItaly

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