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

1997/11/11 by Dmitri V. Alekseevsky, D. V. Alekseevsky, Vicente Cortés +3 · 1 citation
Mathematics · Physics and Astronomy · #53C30 #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #dg-ga #math.DG #msc:53C30

paper · pdf · doi:10.48550/arxiv.dg-ga/9711008

Final version to appear in the Proceedings of the London Mathematical Society; Latex

openalex publication_date 1997/11/11 · arxiv created 1999/05/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Almost abelian pseudo-Kähler Lie algebras

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