| Title:
|
Geodesic graphs on special 7-dimensional g.o. manifolds (English) |
| Author:
|
Dušek, Zdeněk |
| Author:
|
Kowalski, Oldřich |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
42 |
| Issue:
|
5 |
| Year:
|
2006 |
| Pages:
|
213-227 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In ( Dušek, Z., Kowalski, O. and Nikčević, S. Ž., New examples of Riemannian g.o. manifolds in dimension 7, Differential Geom. Appl. 21 (2004), 65–78.), the present authors and S. Nikčević constructed the 2-parameter family of invariant Riemannian metrics on the homogeneous manifolds $M=[{\rm SO}(5)\times {\rm SO}(2)]/{\rm U}(2)$ and $M=[{\rm SO}(4,1)\times {\rm SO}(2)]/{\rm U}(2)$. They proved that, for the open dense subset of this family, the corresponding Riemannian manifolds are g.o. manifolds which are not naturally reductive. Now we are going to investigate the remaining metrics (in the compact case). (English) |
| Keyword:
|
naturally reductive spaces |
| Keyword:
|
Riemannian g.o. spaces |
| Keyword:
|
geodesic graph |
| MSC:
|
53C22 |
| MSC:
|
53C30 |
| idZBL:
|
Zbl 1164.53361 |
| idMR:
|
MR2322408 |
| . |
| Date available:
|
2008-06-06T22:49:29Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108028 |
| . |
| Reference:
|
[1] Dušek Z.: Explicit geodesic graphs on some H-type groups.Rend. Circ. Mat. Palermo, Serie II, Suppl. 69 (2002), 77–88. Zbl 1025.53019, MR 1972426 |
| Reference:
|
[2] Dušek Z., and Kowalski O.: Geodesic graphs on the 13-dimensional group of Heisenberg type.Math. Nachr., 254-255 (2003), 87–96. MR 1983957 |
| Reference:
|
[3] Dušek Z., Kowalski O., Nikčević S. Ž.: New examples of Riemannian g.o. manifolds in dimension 7.Differential Geom. Appl. 21 (2004), 65–78. Zbl 1050.22011, MR 2067459 |
| Reference:
|
[4] Kobayashi S., and Nomizu N.: Foundations of differential geometry - I.Interscience Publishers, New York, 1963. |
| Reference:
|
[5] Kobayashi S., and Nomizu N.: Foundations of differential geometry - II.Interscience Publishers, New York, 1969. |
| Reference:
|
[6] Kowalski O., and Nikčević S. Ž.: On geodesic graphs of Riemannian g.o. spaces.Arch. Math. 73 (1999), 223–234. MR 1705019 |
| Reference:
|
[7] Kowalski O., and Nikčević S. Ž.: On geodesic graphs of Riemannian g.o. spaces - Appendix.Arch. Math. 79 (2002), 158–160. MR 1924152 |
| Reference:
|
[8] Kowalski O., and Vanhecke L.: Riemannian manifolds with homogeneous geodesics.Boll. Un. Math. Ital. B(7)5 (1991), 189–246. MR 1110676 |
| Reference:
|
[9] Szenthe J.: Sur la connection naturelle à torsion nulle.Acta Sci. Math. (Szeged) 38 (1976), 383–398. MR 0431042 |
| . |
