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

Oldřich KowalskiZdeněk Vlášek — 2003

Commentationes Mathematicae Universitatis Carolinae

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).

A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach

Oldřich KowalskiBarbara OpozdaZdeněk Vlášek — 2004

Open Mathematics

The aim of this paper is to classify (lócally) all torsion-less locally homogeneous affine connections on two-dimensional manifolds from a group-theoretical point of view. For this purpose, we are using the classification of all non-equivalent transitive Lie algebras of vector fields in ℝ2 according to P.J. Olver [7].

Homogeneous Geodesics in 3-dimensional Homogeneous Affine Manifolds

Zdeněk DušekOldřich KowalskiZdeněk Vlášek — 2011

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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 connections...

Finite element solution of flows through cascades of profiles in a layer of variable thickness

Miloslav FeistauerJiří FelcmanZdeněk Vlášek — 1986

Aplikace matematiky

The paper is devoted to the numerical modelling of a subsonic irrotational nonviscous flow past a cascade of profiles in a variable thickness fluid layer. It leads to a nonlinear two-dimensional elliptic problem with nonstandard nonhomogeneous boundary conditions. The problem is discretized by the finite element method. Both theoretical and practical questions of the finite element implementation are studied; convergence of the method, numerical integration, iterative methods for the solution of...

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