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Complex extensions of semisimple symmetric spaces
Authors:Laura Geatti
Institution:(1) Dipartimento di Matematica, Università di Roma 2, Tor Vergata, 00133 Roma, Italy
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 ></img>                              </span> to define a <em>G</em>-invariant pseudo-Kähler metric on distinguished <em>G</em>-invariant domains in <span class= ></img>                              </span> or on coverings of principal orbit strata in <span class= ></img>                              </span>. In the rank-one case, we show that the polar map is globally injective and the domain <span class= ></img>                              </span> is an increasing union of <em>q</em>-complete domains.</td>
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