| Title:
|
$\phi({\rm Ric})$-vector fields in Riemannian spaces (English) |
| Author:
|
Hinterleitner, Irena |
| Author:
|
Kiosak, Volodymyr A. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
5 |
| Year:
|
2008 |
| Pages:
|
385-390 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we study vector fields in Riemannian spaces, which satisfy $\nabla \varphi =\mu $, ${\textbf{Ric}}$, $\mu =\mbox {const.}$ We investigate the properties of these fields and the conditions of their coexistence with concircular vector fields. It is shown that in Riemannian spaces, noncollinear concircular and $\varphi (\mbox {\textbf{Ric}})$-vector fields cannot exist simultaneously. It was found that Riemannian spaces with $\varphi (\mbox {\textbf{Ric}})$-vector fields of constant length have constant scalar curvature. The conditions for the existence of $\varphi (\mbox {\textbf{Ric}})$-vector fields in symmetric spaces are given. (English) |
| Keyword:
|
special vector field |
| Keyword:
|
pseudo-Riemannian spaces |
| Keyword:
|
Riemannian spaces |
| Keyword:
|
symmetric spaces |
| Keyword:
|
Kasner metric |
| MSC:
|
53B05 |
| MSC:
|
53B30 |
| idZBL:
|
Zbl 1212.53018 |
| idMR:
|
MR2501574 |
| . |
| Date available:
|
2009-01-29T09:15:59Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127124 |
| . |
| Reference:
|
[1] Brinkmann, H. W.: Einstein spaces which are mapped conformally on each other.Math. Ann. 94 (1) (1925), 119–145. MR 1512246, 10.1007/BF01208647 |
| Reference:
|
[2] Hall, G.: Some remarks on the space-time of Newton and Einstein.Fund. Theories Phys. 153 (2007), 13–29. Zbl 1151.83001, MR 2368238 |
| Reference:
|
[3] Kiosak, V. A.: Equidistant Riemannian spaces. Geometry of generalized spaces.Penz. Gos. Ped. Inst., Penza (1992), 37–41. MR 1265502 |
| Reference:
|
[4] Landau, L. D., Lifschitz, E. M.: Lehrbuch der theoretischen Physik, II, Klassische Feldtheorie.Akademie Verlag, Berlin, 1973. MR 0431969 |
| Reference:
|
[5] Mikeš, J.: Geodesic mappings of affine-connected and Riemannian spaces.J. Math. Sci. 78 (3) (1996), 311–333. MR 1384327, 10.1007/BF02365193 |
| Reference:
|
[6] Mikeš, J., Hinterleitner, I., Kiosak, V. A.: On the theory of geodesic mappings of Einstein spaces and their generalizations.AIP Conf. Proc., 2006, pp. 428–435. |
| Reference:
|
[7] Mikeš, J., Rachůnek, L.: On tensor fields semiconjugated with torse-forming vector fields.Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 44 (2005), 151–160. Zbl 1092.53016, MR 2218574 |
| Reference:
|
[8] Mikeš, J., Škodová, M.: Concircular vector fields on compact spaces.Publ. de la RSME 11 (2007), 302–307. |
| Reference:
|
[9] Shandra, I. G.: Concircular vector fields on semi-riemannian spaces.J. Math. Sci. 31 (2003), 53–68. MR 2464554 |
| Reference:
|
[10] Yano, K.: Concircular Geometry.I-IV. Proc. Imp. Acad., Tokyo, 1940. Zbl 0025.08504 |
| . |
