Abstract
We show that the contact $$(k,\mu )$$ -spaces whose Boeckx invariant is $$\ne 1$$ are realized as real hypersurfaces of the complex quadric $$Q^n$$ and its non-compact dual $$Q^{n*}$$ . Then, we classify simply connected, complete, non-K-contact, CR-symmetric contact metric spaces by real hypersurfaces in Hermitian symmetric spaces.
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