Classification of Stationary Compact Homogeneous Special Pseudo‐Kähler Manifolds of Semisimple Groups

The variation of the Hodge structure of a Calabi–Yau 3‐fold induces a canonical Kähler metric on its Kuranishi moduli space, known as the Weil–Petersson metric. Similarly, special pseudo‐Kähler manifolds correspond to certain (abstract) variations of Hodge structure which generalize the above example. We give the classification of homogeneous special pseudo‐Kähler manifolds of semisimple groups with compact stabilizer. 1991 Mathematics Subject Classification: 53C30, 53C25.