Displaying similar documents to “Homogeneous Geodesics in 3-dimensional Homogeneous Affine Manifolds”

On Metrizable Locally Homogeneous Connections in Dimension

Alena Vanžurová (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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We discuss metrizability of locally homogeneous affine connections on affine 2-manifolds and give some partial answers, using the results from [Arias-Marco, T., Kowalski, O.: Classification of locally homogeneous affine connections with arbitrary torsion on 2-dimensional manifolds. Monatsh. Math. 153 (2008), 1–18.], [Kowalski, O., Opozda, B., Vlášek, Z.: A classification of locally homogeneous connections on 2-dimensional manifolds vis group-theoretical approach. CEJM 2, 1 (2004), 87–102.],...

Homogeneous geodesics in a three-dimensional Lie group

Rosa Anna Marinosci (2002)

Commentationes Mathematicae Universitatis Carolinae

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O. Kowalski and J. Szenthe [KS] proved that every homogeneous Riemannian manifold admits at least one homogeneous geodesic, i.eȯne geodesic which is an orbit of a one-parameter group of isometries. In [KNV] the related two problems were studied and a negative answer was given to both ones: (1) Let M = K / H be a homogeneous Riemannian manifold where K is the largest connected group of isometries and dim M ≥ 3 . Does M always admit more than one homogeneous geodesic? (2) Suppose that M = K / H admits m = dim M linearly...