We present a diamond shaped diagram for even Clifford manifolds similar to the quaternion-Kähler diamond studied by Ch. Boyer and K. Galicki. We define two spaces $${\mathcal {S}}$$ S and $${\mathcal {U}}$$ U which fiber over an even Clifford manifold which, together with the twistor space $${\mathcal {Z}}$$ Z defined by G. Arizmendi and Ch. Hadfield, form a diamond shaped diagram of fibrations. Moreover, we prove that, under certain natural conditions, $${\mathcal {Z}}$$ Z is Kahler–Einstein, $${\mathcal {S}}$$ S is Sasaki–Einstein and $${\mathcal {U}}$$ U is special-Kähler.

中文翻译：

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均匀的克利福德钻石

我们甚至为 Clifford 流形提供了一个菱形图，类似于 Ch 研究的四元数-Kähler 金刚石。博耶和 K. Galicki。我们定义了两个空间 $${\mathcal {S}}$$ S 和 $${\mathcal {U}}$$ U，它们在偶数 Clifford 流形上纤维化，与扭曲空间 $${\mathcal {Z }}$$ Z 由 G. Arizmendi 和 Ch 定义。Hadfield，形成一个菱形的纤维化图。此外，我们证明，在一定的自然条件下，$${\mathcal {Z}}$$ Z 是 Kahler-Einstein，$${\mathcal {S}}$$ S 是 Sasaki-Einstein，$${\mathcal {U}}$$ U 是特别的-Kähler。