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manuscripta mathematica

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

Complex extensions of semisimple symmetric spaces

  • Laura GeattiEmail author
Article

Abstract

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.

Keywords

Number Theory Symmetric Space Algebraic Geometry Topological Group Tangent Bundle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di Roma 2RomaItaly

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