| Title:
|
On geodesic mappings preserving the Einstein tensor (English) |
| Author:
|
Chepurna, Olena E. |
| Author:
|
Kiosak, Volodymyr A. |
| Author:
|
Mikeš, Josef |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
49 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
49-52 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper there are discussed the geodesic mappings which preserved the Einstein tensor. We proved that the tensor of concircular curvature is invariant under Einstein tensor-preserving geodesic mappings. (English) |
| Keyword:
|
Geodesic mapping |
| Keyword:
|
Einstein tensor |
| MSC:
|
53B20 |
| MSC:
|
53B30 |
| idZBL:
|
Zbl 1228.53020 |
| idMR:
|
MR2796946 |
| . |
| Date available:
|
2011-02-18T07:35:55Z |
| Last updated:
|
2013-09-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141416 |
| . |
| Reference:
|
[1] Chepurna, O., Kiosak, V., Mikeš, J: Conformal mappings of Riemannian spaces which preserve the Einstein tensor. J. Appl. Math. Aplimat 3, 1 (2010), 253–258. |
| Reference:
|
[2] Mikeš, J.: On geodesic mappings of Einstein spaces. Math. Notes 28 (1981), 922–923, Translation of Mat. Zametki 28 (1980), 935–938. MR 0603226, 10.1007/BF01709156 |
| Reference:
|
[3] Mikeš, J.: Geodesic mappings of affine-connected and Riemannian spaces. J. Math. Sci. 78, 3 (1996), 311–333. MR 1384327, 10.1007/BF02365193 |
| Reference:
|
[4] Mikeš, J., Hinterleitner, I., Kiosak, V.: On the theory of geodesic mappings of Einstein spaces and their generalizations. AIP Conf. Proc. 861 (2006), 428–435. |
| Reference:
|
[5] Mikeš, J., Kiosak, V. A., Vanžurová, A.: Geodesic mappings of manifolds with affine connection. Palacky University Press, Olomouc, 2008. Zbl 1176.53004, MR 2488821 |
| Reference:
|
[6] Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic mappings and some generalizations. Palacky University Press, Olomouc, 2009. Zbl 1222.53002, MR 2682926 |
| Reference:
|
[7] Sinyukov, N. S.: Geodesic mappings of Riemannian spaces. Nauka, Moscow, 1979. Zbl 0637.53020, MR 0552022 |
| Reference:
|
[8] Yano, K.: Concircular Geometry. Proc. Imp. Acad. 16 (Tokyo), (1940), 195–200, 354–360, 442–448, 505–511. Zbl 0025.08504 |
| . |
