Classification of stationary compact homogeneous special pseudo Kähler manifolds of semisimple groups

Abstract

The variation of 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.