Classification of locally projectively homogeneous torsion-less affine connections in the plane domains.
Berechnung der ebenen Potentialströmung von rotierenden radialen Profilgittern
On double-ruled hypersurfaces in
We classify locally the induced Riemannian metrics of all irreducible double-ruled hypersurfaces in .
On the local moduli space of locally homogeneous affine connections in plane domains
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).
On special Riemannian -manifolds with distinct constant Ricci eigenvalues
The first author and F. Prufer gave an explicit classification of all Riemannian 3-manifolds with distinct constant Ricci eigenvalues and satisfying additional geometrical conditions. The aim of the present paper is to get the same classification under weaker geometrical conditions.
A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach
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].
Curvature homogeneity of affine connections on two-dimensional manifolds
Curvature homogeneity of (torsion-free) affine connections on manifolds is an adaptation of a concept introduced by I. M. Singer. We analyze completely the relationship between curvature homogeneity of higher order and local homogeneity on two-dimensional manifolds.
Finite element solution of flows through cascades of profiles in a layer of variable thickness
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...
Homogeneous Geodesics in 3-dimensional Homogeneous Affine Manifolds
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...
Nedožité sedmdesátiny Prof. RNDr. Břetislava Nováka, DrSc. (1938-2003)
Prof. RNDr. Břetislav Novák, DrSc. (1938–2003) would be seventy
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