Zdeněk Vlášek

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].

Finite-element solution of flow problems with trailing conditions

Abstract The paper deals with the finite-element solution of stream function problems describing nonviscous subsonic irrotational flows past profiles. The main emphasis is laid on the treatment of the nonstandard trailing stagnation conditions which lead to physically admissible solutions. The paper presents a general conception of stream function finite-element modelling of complicated flow problems and a complete theory of the finite-element approximations, including the investigation of the existence and uniqueness of the solution of the nonsymmetric discrete problem and the convergence of approximate solutions to the exact solution.

On Locally Nonhomogeneous Pseudo–Riemannian Manifolds with Locally Homogeneous Levi–Civita Connections

In this paper we make the first steps to a classification of (pseudo-) Riemannian manifolds which are not locally homogeneous but their Levi–Civita connections are homogeneous. The full classification is given for dimension n = 2; in higher dimensions we prove some substantial partial results. In more generality, we are also interested in the difference between the dimension of the algebra of affine Killing vector fields and that of the algebra of metric Killing vector fields (without any homogeneity properties).

Homogeneous Einstein metrics on Aloff-Wallach spaces

Abstract All homogeneous Einstein metrics on 7-dimensional Aloff-Wallach spaces N k , l are described. For some of these spaces, the existence of homogeneous Einstein metrics with positive sectional curvature is proved.

On 3D-Riemannian Manifolds with Prescribed Ricci Eigenvalues

In this paper, we deal with 3-dimensional Riemannian manifolds where some conditions are put on their principal Ricci curvatures. In Section 2 we classify locally all Riemannian 3-manifolds with prescribed distinct Ricci eigenvalues, which can be given as arbitrary real analytic functions. In Section 3 we recall, for the constant distinct Ricci eigenvalues, an explicit solution of the problem, but in a more compact form than it was presented in [17]. Finally, in Section 4 we give a survey of related results, mostly published earlier in various journals. Last but not least, we compare various PDE methods used for solving problems of this kind.