Classification of stationary compact homogeneous special pseudo K\"ahler manifolds of semisimple groups

TL;DR

This paper classifies stationary, compact, homogeneous special pseudo K"ahler manifolds associated with semisimple groups, extending the understanding of their geometric structures and symmetries.

Contribution

It provides a complete classification of such manifolds, highlighting their structure and relation to variations of Hodge structure.

Findings

Classification of homogeneous special pseudo K"ahler manifolds achieved

Identification of semisimple groups with compact stabilizers in this context

Extension of Hodge structure variations to pseudo K"ahler geometry

Abstract

The variation of Hodge structure of a Calabi-Yau 3-fold induces a canonical K\"ahler metric on its Kuranishi moduli space, known as the Weil-Petersson metric. Similarly, special pseudo K\"ahler manifolds correspond to certain (abstract) variations of Hodge structure which generalize the above example. We give the classification of homogeneous special pseudo K\"ahler manifolds of semisimple groups with compact stabilizer.