Lorentzian homogeneous structures with indecomposable holonomy
arxiv(2024)
摘要
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.
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