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.
@article{107567, author = {Yurii G. Nikonorov and Eugene D. Rodionov}, title = {Standard homogeneous Einstein manifolds and Diophantine equations}, journal = {Archivum Mathematicum}, volume = {032}, year = {1996}, pages = {123-136}, zbl = {0903.53033}, mrnumber = {1407344}, language = {en}, url = {http://dml.mathdoc.fr/item/107567} }
Nikonorov, Yurii G.; Rodionov, Eugene D. Standard homogeneous Einstein manifolds and Diophantine equations. Archivum Mathematicum, Tome 032 (1996) pp. 123-136. http://gdmltest.u-ga.fr/item/107567/
Geometry of Lie groups and symmetric spaces, IL, Moscow, 1949 (Russian). (1949)
Homogeneous Riemannian manifolds with irreducible isotropy group, Trudy Sem. Vektor. Tensor. Anal. Vyp. 13 (1966), 68-145 (Russian). (1966) | MR 0210031
The geometry and structure of isotropy irreducible homogeneous spaces, Acta Math., 120 (1968), 59-148. (1968) | MR 0223501
On normal homogeneous Einstein manifolds, Ann. Sci. Ecole Norm. Sup. (4) 18 (1985), 563-633. (1985) | MR 0839687 | Zbl 0598.53049
Standard homogeneous Einstein manifolds, Russian Acad. Sci. Dokl. Math. 47 (1993), no.1, 37-40. (1993) | MR 1216925 | Zbl 0826.53044
Homogeneous Riemannian manifolds with Einstein metrics, Doctor dissertation in Mathematics, Institute of Mathematics, Novosibirsk, 1994. (1994)
A Classical Introduction to Modern Number Theory, Berlin: Springer-Verlag, 1993. (1993) | MR 1070716
Semi-simple Subalgebras of Semi-simple Lie Algebras, Transl. Amer. Math. Soc., Series 2, 6 (1957), 111-244. (1957)