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Currently displaying 1 – 3 of 3

Order by Relevance | Title | Year of publication

On a classification of almost geodesic mappings of affine connection spaces

Vladimir Berezovskij; Josef Mikeš — 1996

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

On special almost geodesic mappings of type $π_{1}$ of spaces with affine connection

Vladimir Berezovskij; Josef Mikeš — 2004

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

N. S. Sinyukov [5] introduced the concept of an of a space $A_{n}$ with an affine connection without torsion onto ${\bar{A}}_{n}$ and found three types: $π_{1}$ , $π_{2}$ and $π_{3}$ . The authors of [1] proved completness of that classification for $n > 5$ .By definition, special types of mappings $π_{1}$ are characterized by equations $P_{i j, k}^{h} + P_{i j}^{α} P_{α k}^{h} = a_{i j} δ_{k}^{h},$ where $P_{i j}^{h} \equiv {\bar{Γ}}_{i j}^{h} - Γ_{i j}^{h}$ is the deformation tensor of affine connections of the spaces $A_{n}$ and ${\bar{A}}_{n}$ .In this paper geometric objects which preserve these mappings are found and also closed classes of such spaces are described.

On almost geodesic mappings of the type $π_{1}$ of Riemannian spaces preserving a system $n$ -orthogonal hypersurfaces

Berezovskij, Vladimir; Mikeš, Josef — 1999

Proceedings of the 18th Winter School "Geometry and Physics"

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