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Homogeneous geodesics of non-reductive homogeneous pseudo-Riemannian 4-manifolds. (English) Zbl 1318.53048

The authors consider invariant metrics on four-dimensional non-reductive homogeneous pseudo-Riemannian manifolds. They give an explicit classification of Killing and geodesic vector fields (using a lot of calculations with Maple 16) and find homogeneous geodesics. Then they give an explicit classification of four-dimensional non-reductive homogeneous pseudo-Riemannian geodesic orbit spaces. Finally, they determine the possible holonomy Lie algebras of the invariant metrics.

MSC:

53C30 Differential geometry of homogeneous manifolds
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C22 Geodesics in global differential geometry
53C29 Issues of holonomy in differential geometry

Software:

Maple
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Full Text: DOI

References:

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