Totally geodesic and parallel hypersurfaces of four-dimensional oscillator groups

DOI10.1007/s00025-012-0304-4zbMath1279.53056OpenAlexW1971587911MaRDI QIDQ370816

Joeri Van der Veken, Giovanni Calvaruso

Publication date: 19 September 2013

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-012-0304-4

zbMATH Keywords

totally geodesic hypersurfaceoscillator groupparallel hypersurface

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Differential geometry of symmetric spaces (53C35) Lie groups (22E99)

Related Items (9)

Kundt three-dimensional left invariant spacetimes ⋮ Oscillator spacetimes are Ricci solitons ⋮ On the geometry of higher dimensional Heisenberg groups ⋮ On the symmetries of the Lorentzian oscillator group ⋮ Totally geodesic and parallel hypersurfaces of Gödel-type spacetimes ⋮ Lorentzian symmetric spaces which are Einstein-Yang-Mills with respect to invariant metric connections ⋮ Poisson algebras and symmetric Leibniz bialgebra structures on oscillator Lie algebras ⋮ On the geometrical properties of hypercomplex four-dimensional Lie groups ⋮ Parallel and totally geodesic hypersurfaces of 5-dimensional 2-step homogeneous nilmanifolds

Cites Work

• Unnamed Item
• Methods of investigation of the causal structures of homogeneous Lorentz manifolds
• Parallel surfaces in three-dimensional Lorentzian Lie groups
• Groupes de Lie munis de métriques bi-invariantes. (Lie groups admitting bi-invariant metrics)
• Chronogeometry of an electromagnetic wave given by a bi-invariant metric on the oscillator group
• Symmetric submanifolds of compact symmetric spaces
• Geometry of oscillator groups and locally symmetric manifolds
• Homogeneous Lorentzian structures on the oscillator groups
• The representations of the oscillator group
• LORENTZIAN SYMMETRIC THREE-SPACES AND THE CLASSIFICATION OF THEIR PARALLEL SURFACES
• Reductive decompositions and Einstein–Yang–Mills equations associated to the oscillator group

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