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This article continues a line of research aimed at solving an importantproblem of T. Kobayashi of the existence of compact Clifford-Klein forms ofreductive homogeneous spaces. We contribute to this topic by showing thatalmost all symmetric spaces and 3-symmetric spaces do not admit solvablecompact CliffordfKlein forms (with several possible exceptions). Our basic toolis a combination of the Hirzebruch-Kobayashi-Ono proportionality principle withthe theory of syndetic hulls. Using this, we prove a general theorem whichyields a sufficient condition for the non-existence of compact solvableCliffordKlein forms.

On the Hirzebruch-Kobayashi-Ono proportionality principle and the  non-existence of compact solvable Clifford-Klein forms of certain homogeneous  spaces