On special almost geodesic mappings of type ${\pi }_1$ of spaces with affine connection

Berezovskij, Vladimir, and Mikeš, Josef. "On special almost geodesic mappings of type $\pi _1$ of spaces with affine connection." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 43.1 (2004): 21-26. <http://eudml.org/doc/32360>.

@article{Berezovskij2004,
abstract = {N. S. Sinyukov [5] introduced the concept of an almost geodesic mapping of a space $A_n$ with an affine connection without torsion onto $\overline\{A\}_n$ and found three types: $\pi _1$, $\pi _2$ and $\pi _3$. The authors of [1] proved completness of that classification for $n>5$.By definition, special types of mappings $\pi _1$ are characterized by equations \[ P\_\{ij,k\}^h+P\_\{ij\}^\alpha P\_\{\alpha k\}^h =a\_\{ij\} \delta \_\{k\}^h , \] where $P_\{ij\}^h\equiv \overline\{\Gamma \}_\{ij\}^h-\Gamma _\{ij\}^h$ is the deformation tensor of affine connections of the spaces $A_n$ and $\overline\{A\}_n$.In this paper geometric objects which preserve these mappings are found and also closed classes of such spaces are described.},
author = {Berezovskij, Vladimir, Mikeš, Josef},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {almost geodesic mappings; affine connection space; almost geodesic mappings; affine connection space},
language = {eng},
number = {1},
pages = {21-26},
publisher = {Palacký University Olomouc},
title = {On special almost geodesic mappings of type $\pi _1$ of spaces with affine connection},
url = {http://eudml.org/doc/32360},
volume = {43},
year = {2004},
}

TY - JOUR
AU - Berezovskij, Vladimir
AU - Mikeš, Josef
TI - On special almost geodesic mappings of type $\pi _1$ of spaces with affine connection
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2004
PB - Palacký University Olomouc
VL - 43
IS - 1
SP - 21
EP - 26
AB - N. S. Sinyukov [5] introduced the concept of an almost geodesic mapping of a space $A_n$ with an affine connection without torsion onto $\overline{A}_n$ and found three types: $\pi _1$, $\pi _2$ and $\pi _3$. The authors of [1] proved completness of that classification for $n>5$.By definition, special types of mappings $\pi _1$ are characterized by equations \[ P_{ij,k}^h+P_{ij}^\alpha P_{\alpha k}^h =a_{ij} \delta _{k}^h , \] where $P_{ij}^h\equiv \overline{\Gamma }_{ij}^h-\Gamma _{ij}^h$ is the deformation tensor of affine connections of the spaces $A_n$ and $\overline{A}_n$.In this paper geometric objects which preserve these mappings are found and also closed classes of such spaces are described.
LA - eng
KW - almost geodesic mappings; affine connection space; almost geodesic mappings; affine connection space
UR - http://eudml.org/doc/32360
ER -