Isotropy irreducible spaces are first introduced by Riemannian geometers, as homogeneous real manifolds carrying a canonical invariant metric. Such spaces are classified by Manturov (1960s), Wolf (1968) and Krämer (1975), and their classification provides a number of interesting new examples, for example satisfying the Einstein condition. In this talk, I will introduce a complexified version of isotropy irreducible space, which is called isotropy irreducible variety. In the first half, I will explain geometric properties of isotropy irreducible varieties, and give several non-classical examples belonging to algebraic geometry. Next, I will present a connection between isotropy irreducible varieties and complex contact geometry, which has not been observed in the real setting.
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