| Title:
|
$g$-natural metrics of constant curvature on unit tangent sphere bundles (English) |
| Author:
|
Abbassi, M. T. K. |
| Author:
|
Calvaruso, G. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
48 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
81-95 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We completely classify Riemannian $g$-natural metrics of constant sectional curvature on the unit tangent sphere bundle $T_1 M$ of a Riemannian manifold $(M,g)$. Since the base manifold $M$ turns out to be necessarily two-dimensional, weaker curvature conditions are also investigated for a Riemannian $g$-natural metric on the unit tangent sphere bundle of a Riemannian surface. (English) |
| Keyword:
|
unit tangent sphere bundle |
| Keyword:
|
$g$-natural metric |
| Keyword:
|
curvature tensor |
| Keyword:
|
contact metric geometry |
| MSC:
|
53C15 |
| MSC:
|
53C25 |
| MSC:
|
53D10 |
| idMR:
|
MR2946208 |
| DOI:
|
10.5817/AM2012-2-81 |
| . |
| Date available:
|
2012-06-08T08:29:51Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142821 |
| . |
| Reference:
|
[1] Abbassi, K. M. T., Calvaruso, G.: $g$–natural contact metrics on unit tangent sphere bundles.Monaths. Math. 151 (2006), 89–109. 10.1007/s00605-006-0421-9 |
| Reference:
|
[2] Abbassi, K. M. T., Calvaruso, G.: The curvature tensor of $g$-natural metrics on unit tangent sphere bundles.Int. J. Contemp. Math. Sci. 6 (3) (2008), 245–258. Zbl 1148.53018, MR 2400090 |
| Reference:
|
[3] Abbassi, K. M. T., Kowalski, O.: Naturality of homogeneous metrics on Stiefel manifolds $SO(m+1)/SO(m-1)$.Differential Geom. Appl. 28 (2010), 131–139. Zbl 1190.53020, MR 2594457, 10.1016/j.difgeo.2009.05.007 |
| Reference:
|
[4] Abbassi, K. M. T., Sarih, M.: On natural metrics on tangent bundles of Riemannian manifolds.Arch. Math. (Brno) 41 (2005), 71–92. Zbl 1114.53015, MR 2142144 |
| Reference:
|
[5] Abbassi, K. M. T., Sarih, M.: On some hereditary properties of Riemannian $g$-natural metrics on tangent bundles of Riemannian manifolds.Differential Geom. Appl. 22 (1) (2005), 19–47. Zbl 1068.53016, MR 2106375 |
| Reference:
|
[6] Boeckx, E., Vanhecke, L.: Unit tangent bundles with constant scalar curvature.Czechoslovak Math. J. 51 (2001), 523–544. MR 1851545, 10.1023/A:1013779805244 |
| Reference:
|
[7] Calvaruso, G.: Contact metric geometry of the unit tangent sphere bundle. In: Complex, Contact and Symmetric manifolds, in Honor of L. Vanhecke.: Complex, Contact and Symmetric manifolds, in Honor of L. Vanhecke, Progr. Math. 234 (2005), 271–285. MR 2105140 |
| Reference:
|
[8] Kolář, I., Michor, P. W., Slovák, J.: Natural operations in differential geometry.Springer–Verlag, Berlin, 1993. Zbl 0782.53013, MR 1202431 |
| Reference:
|
[9] Kowalski, O.: On curvature homogeneous spaces.Publ. Dep. Geom. Topologia, Univ. Santiago Compostela (Cordero, L. A. et al., ed.), 1998, pp. 193–205. Zbl 0911.53030 |
| Reference:
|
[10] Kowalski, O., Sekizawa, M.: Natural transformations of Riemannian metrics on manifolds to metrics on tangent bundles – a classification.Bull. Tokyo Gakugei Univ. (4) 40 (1988), 1–29. Zbl 0656.53021, MR 0974641 |
| . |
