| Title:
|
Naturally reductive homogeneous $(\alpha ,\beta )$-metric spaces (English) |
| Author:
|
Parhizkar, M. |
| Author:
|
Salimi Moghaddam, H.R. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2021 |
| Pages:
|
1-11 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper we study naturally reductive homogeneous $(\alpha ,\beta )$-metric spaces. We show that for homogeneous $(\alpha ,\beta )$-metric spaces, under a mild condition, the two definitions of naturally reductive homogeneous Finsler space, given in the literature, are equivalent. Then, we compute the flag curvature of naturally reductive homogeneous $(\alpha ,\beta )$-metric spaces. (English) |
| Keyword:
|
naturally reductive homogeneous space |
| Keyword:
|
invariant Riemannian metric |
| Keyword:
|
invariant $(\alpha ,\beta )$-metric |
| MSC:
|
53C30 |
| MSC:
|
53C60 |
| idZBL:
|
Zbl 07332700 |
| idMR:
|
MR4260836 |
| DOI:
|
10.5817/AM2021-1-1 |
| . |
| Date available:
|
2021-03-05T10:30:16Z |
| Last updated:
|
2021-11-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148712 |
| . |
| Reference:
|
[1] Asanov, G.S.: Finsleroid space with angle and scalar product.Publ. Math. Debrecen 67 (2005), 209–252. MR 2163126 |
| Reference:
|
[2] Asanov, G.S.: Finsleroid Finsler spaces of positive-definite and relativistic type.Rep. Math. Phys. 58 (2006), 275–300. MR 2281541, 10.1016/S0034-4877(06)80053-4 |
| Reference:
|
[3] Bao, D., Chern, S.S., Shen, Z.: An Introduction to Riemann-Finsler Geometry.Springer, Berlin, 2000. Zbl 0954.53001, MR 1747675 |
| Reference:
|
[4] Chern, S.S., Shen, Z.: Riemann-Finsler geometry.Nankai Tracts in Mathematics, vol. 6, World Scientific, 2005. MR 2169595 |
| Reference:
|
[5] Deng, S., Hou, Z.: Invariant Finsler metrics on homogeneous manifolds.J. Phys. A: Math. Gen. 37 (2004), 8245–8253. Zbl 1062.58007, MR 2092795, 10.1088/0305-4470/37/34/004 |
| Reference:
|
[6] Deng, S., Hou, Z.: Invariant Randers metrics on homogeneous Riemannian manifolds.J. Phys. A: Math. Gen. 37 (2004), 4353–4360. Zbl 1049.83005, MR 2063598, 10.1088/0305-4470/37/15/004 |
| Reference:
|
[7] Deng, S., Hou, Z.: Naturally reductive homogeneous Finsler spaces.Manuscripta Math. 131 (2010), 215–229. MR 2574999, 10.1007/s00229-009-0314-z |
| Reference:
|
[8] Kikuchi, S.: On the condition that a space with $ (\alpha ,\beta ) $-metric be locally Minkowskian.Tensor, N.S. 33 (1979), 142–246. MR 0577431 |
| Reference:
|
[9] Kobayashi, S., Nomizu, K.: Foundations of differential geometry.Wiley-Interscience, New York, 1969. Zbl 0175.48504, MR 0152974 |
| Reference:
|
[10] Latifi, D.: Homogeneous geodesics in homogeneous Finsler spaces.J. Geom. Phys. 57 (2007), 1421–1433. MR 2289656, 10.1016/j.geomphys.2006.11.004 |
| Reference:
|
[11] Latifi, D.: Naturally reductive homogeneous Randers spaces.J. Geom. Phys. 60 (2010), 1968–1973. MR 2735283, 10.1016/j.geomphys.2010.08.002 |
| Reference:
|
[12] Matsumoto, M.: The Berwald connection of a Finsler space with an $ (\alpha ,\beta ) $-metric.Tensor, N.S. 50 (1991), 18–21. MR 1156480 |
| Reference:
|
[13] Matsumoto, M.: Theory of Finsler spaces with $(\alpha ,\beta )$-metric.Rep. Math. Phys. 31 (1992), 43–83. MR 1208489, 10.1016/0034-4877(92)90005-L |
| Reference:
|
[14] Moghaddam, H.R. Salimi: The flag curvature of invariant $(\alpha ,\beta )-$metrics of type $\frac{(\alpha +\beta )^2}{\alpha }$.J. Phys. A: Math. Theor. 41 (2008), 6 pp., 275206. MR 2455543, 10.1088/1751-8113/41/27/275206 |
| Reference:
|
[15] Randers, G.: On an asymmetrical metric in the four-space of general relativity.On an asymmetrical metric in the four-space of general relativity 59 (1941), 195–199. Zbl 0027.18101, MR 0003371 |
| Reference:
|
[16] Shen, Z.: Lectures on Finsler Geometry.World Scientific, 2001. Zbl 0974.53002, MR 1845637 |
| . |
