Lorentzian homogeneous structures with indecomposable holonomy
Steven Greenwood, Thomas Leistner
Source abstract
Abstract For a Lorentzian homogeneous space, we study how algebraic conditions on the isotropy group affect the geometry and curvature of the homogeneous space. More specifically, we prove that a Lorentzian locally homogeneous space is locally isometric to a plane wave if it admits an Ambrose–Singer connection with indecomposable, non‐irreducible holonomy. This generalises several existing results that require a certain algebraic type of the torsion of the Ambrose–Singer connection and moreover is in analogy to the fact that a Lorentzian homogeneous space with irreducible isotropy has constant sectional curvature. In addition, we prove results about Lorentzian connections with parallel torsion and for 2‐symmetric connections.
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