| Title:
|
On special almost geodesic mappings of type $\pi_1$ of spaces with affine connection (English) |
| Author:
|
Berezovsky, Vladimir |
| Author:
|
Mikeš, Josef |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
21-26 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
N.~S.~Sinyukov [5] introduced the concept of an {\em 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 $n>5$.\par 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 $\overline{A}_n$.\par In this paper geometric objects which preserve these mappings are found and also closed classes of such spaces are described. (English) |
| Keyword:
|
almost geodesic mappings |
| Keyword:
|
affine connection space |
| MSC:
|
53B05 |
| MSC:
|
53B99 |
| idZBL:
|
Zbl 1073.53023 |
| idMR:
|
MR2124599 |
| . |
| Date available:
|
2009-08-21T12:53:43Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/132950 |
| . |
| Reference:
|
[1] Berezovsky V. E., Mikeš J.: On the classification of almost geodesic mappings of affine-connected spaces.In: Proc. Conf., Dubrovnik (Yugoslavia) 1988, 41–48 (1989). MR 1040054 |
| Reference:
|
[2] Berezovsky V. E., Mikeš J.: On almost geodesic mappings of the type $\pi _1$ of Riemannian spaces preserving a system $n$-orthogonal hypersurfaces.Suppl. Rend. Circ. Mat. Palermo, II. Ser. 59, 103–108 (1999). MR 1692261 |
| Reference:
|
[3] Chernyshenko V. M.: Räume mit einem speziellen Komplex von geodätischen Linien.Tr. Semin. Vektor. Tenzor. Anal. 11 (1961), 253–268 (in Russian). Zbl 0156.41804 |
| Reference:
|
[4] Mikeš J.: Holomorphically projective mappings and their generalizations.J. Math. Sci., New York 89, 3 (1998), 1334–1353. Zbl 0983.53013, MR 1619720 |
| Reference:
|
[5] Sinyukov N. S.: On geodesic mappings of Riemannian spaces. : Nauka, Moscow., 1979 (in Russian). MR 0552022 |
| Reference:
|
[6] Sinyukov N. S.: Almost geodesic mappings of affine connected and Riemannian spaces.Itogi Nauki Tekh., Ser. Probl. Geom. 13 (1982), 3–26 (in Russian); J. Sov. Math. 25 (1984), 1235–1249. Zbl 0498.53010, MR 0674123 |
| . |
