Displaying similar documents to “On Metrizable Locally Homogeneous Connections in Dimension”

On the local moduli space of locally homogeneous affine connections in plane domains

Oldřich Kowalski, Zdeněk Vlášek (2003)

Commentationes Mathematicae Universitatis Carolinae

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Classification of locally homogeneous affine connections in two dimensions is a nontrivial problem. (See [] and [] for two different versions of the solution.) Using a basic formula by B. Opozda, [], we prove that all locally homogeneous torsion-less affine connections defined in open domains of a 2-dimensional manifold depend essentially on at most 4 parameters (see Theorem 2.4).

Homogeneous Geodesics in 3-dimensional Homogeneous Affine Manifolds

Zdeněk Dušek, Oldřich Kowalski, Zdeněk Vlášek (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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For studying homogeneous geodesics in Riemannian and pseudo-Riemannian geometry (on reductive homogeneous spaces) there is a simple algebraic formula which works, at least potentially, in every given case. In the affine differential geometry, there is not such a universal formula. In the previous work, we proposed a simple method of investigation of homogeneous geodesics in homogeneous affine manifolds in dimension 2. In the present paper, we use this method on certain classes of homogeneous...