| Title:
|
Standard homogeneous Einstein manifolds and Diophantine equations (English) |
| Author:
|
Nikonorov, Yurii G. |
| Author:
|
Rodionov, Eugene D. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
32 |
| Issue:
|
2 |
| Year:
|
1996 |
| Pages:
|
123-136 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Some new examples of standard homogeneous Einstein manifolds with semisimple transitive groups of motions and semisimple isotropy subgroups are constructed. For the construction of these examples the solutions of some systems of Diophantine equations are used. (English) |
| Keyword:
|
Riemannian manifolds |
| Keyword:
|
homogeneous spaces |
| Keyword:
|
Einstein metrics |
| MSC:
|
11D09 |
| MSC:
|
53C25 |
| MSC:
|
53C30 |
| idZBL:
|
Zbl 0903.53033 |
| idMR:
|
MR1407344 |
| . |
| Date available:
|
2008-06-06T21:30:32Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107567 |
| . |
| Reference:
|
[1] Cartan É.: Geometry of Lie groups and symmetric spaces.IL, Moscow, 1949 (Russian). |
| Reference:
|
[2] Manturov O. V.: Homogeneous Riemannian manifolds with irreducible isotropy group.Trudy Sem. Vektor. Tensor. Anal. Vyp. 13 (1966), 68-145 (Russian). MR 0210031 |
| Reference:
|
[3] Joseph A. Wolf: The geometry and structure of isotropy irreducible homogeneous spaces.Acta Math., 120 (1968), 59-148. MR 0223501 |
| Reference:
|
[4] McKenzie Y. W., Ziller W.: On normal homogeneous Einstein manifolds.Ann. Sci. Ecole Norm. Sup. (4) 18 (1985), 563-633. Zbl 0598.53049, MR 0839687 |
| Reference:
|
[5] Rodionov E. D.: Standard homogeneous Einstein manifolds.Russian Acad. Sci. Dokl. Math. 47 (1993), no.1, 37-40. Zbl 0826.53044, MR 1216925 |
| Reference:
|
[6] Rodionov E. D.: Homogeneous Riemannian manifolds with Einstein metrics.Doctor dissertation in Mathematics, Institute of Mathematics, Novosibirsk, 1994. |
| Reference:
|
[7] Ireland K., Rosen M.: A Classical Introduction to Modern Number Theory.Berlin: Springer-Verlag, 1993. MR 1070716 |
| Reference:
|
[8] Dynkin E. B.: Semi-simple Subalgebras of Semi-simple Lie Algebras.Transl. Amer. Math. Soc., Series 2, 6 (1957), 111-244. |
| . |
