Classification of connected holonomy groups of pseudo-K "ahlerian\n manifolds of index 2

2004/05/06 by Anton S. Galaev, Galaev, Anton S.
Mathematics · Physics and Astronomy · #53B30 #53C29 #53C50 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0405098

openalex publication_date 2004/05/06 · openalex created_date 2022/09/10 · openalex updated_date 2026/07/28

Abstract

The problem of classification of connected holonomy groups (equivalently of\nholonomy algebras) for pseudo-Riemannian manifolds is open. The classification\nof Riemannian holonomy algebras is a classical result. The classification of\nLorentzian holonomy algebras was obtained recently.\n In the present paper weakly-irreducible not irreducible subalgebras of\n su(1,n+1) (n\≥ 0) are classified. Weakly-irreducible not irreducible\nholonomy algebras of pseudo-K "ahlerian and special pseudo-K "ahlerian\nmanifolds are classified. An example of metric for each possible holonomy\nalgebra is given. This gives the classification of holonomy algebras for\npseudo-K "ahlerian manifolds of index 2\n

Citations

• A theorem on holonomy

Related

• Holonomy groups and special geometric structures of pseudo-Kählerian manifolds of index 2
• Holonomy in pseudo-Hermitian geometry
• Parallel spinors and holonomy groups on pseudo-Riemannian spinmanifolds
• Holonomy groups of G₂^*-manifolds
• Riemannian Holonomy and Algebraic Geometry