Complex crowns of Riemannian symmetric spaces and non-compactly causal symmetric spaces

Abstract

In this paper we define a distinguished boundary for the complex crowns $Ξ\subeq G_\C /K_\C$ of non-compact Riemannian symmetric spaces $G/K$. The basic result is that affine symmetric spaces of $G$ can appear as a component of this boundary if and only if they are non-compactly causal symmetric spaces.