Geodesic
Invariant Einstein Metrics on Three-Locally-Symmetric Spaces
Matematičeskie trudy, Tome 6 (2003) no. 2, pp. 80-101 
A. M. Lomshakov; Yu. G. Nikonorov; E. V. Firsov. Invariant Einstein Metrics on Three-Locally-Symmetric Spaces. Matematičeskie trudy, Tome 6 (2003) no. 2, pp. 80-101. http://geodesic.mathdoc.fr/item/MT_2003_6_2_a3/
@article{MT_2003_6_2_a3,
     author = {A. M. Lomshakov and Yu. G. Nikonorov and E. V. Firsov},
     title = {Invariant {Einstein} {Metrics} on {Three-Locally-Symmetric} {Spaces}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {80--101},
     year = {2003},
     volume = {6},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2003_6_2_a3/}
}
TY  - JOUR
AU  - A. M. Lomshakov
AU  - Yu. G. Nikonorov
AU  - E. V. Firsov
TI  - Invariant Einstein Metrics on Three-Locally-Symmetric Spaces
JO  - Matematičeskie trudy
PY  - 2003
SP  - 80
EP  - 101
VL  - 6
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MT_2003_6_2_a3/
LA  - ru
ID  - MT_2003_6_2_a3
ER  - 
%0 Journal Article
%A A. M. Lomshakov
%A Yu. G. Nikonorov
%A E. V. Firsov
%T Invariant Einstein Metrics on Three-Locally-Symmetric Spaces
%J Matematičeskie trudy
%D 2003
%P 80-101
%V 6
%N 2
%U http://geodesic.mathdoc.fr/item/MT_2003_6_2_a3/
%G ru
%F MT_2003_6_2_a3

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the problem of existence and the number of invariant Einstein metrics on three-locally-symmetric spaces. We prove that if there are no isomorphic modules in the isotropy decomposition then the number of invariant Einstein metrics (up to isometry and homothety) varies from one to four. Basing on these results, we construct new examples of Einstein metrics.

[1] Besse A. L., Mnogoobraziya Einshteina, Mir, M., 1990

[2] Varden van der B. L., Algebra, Nauka, M., 1972

[3] Demidovich B. P., Maron I. A., Osnovy vychislitelnoi matematiki, Nauka, M., 1966

[4] Nikonorov Yu. G., “Ob odnom klasse odnorodnykh kompaktnykh mnogoobrazii Einshteina”, Sib. mat. zhurn., 41:1 (2000), 200–205 | MR | Zbl

[5] Rodionov E. D., “Einshteinovy metriki na chetnomernykh odnorodnykh prostranstvakh, dopuskayuschikh odnorodnuyu rimanovu metriku polozhitelnoi sektsionnoi krivizny”, Sib. mat. zhurn., 32:3 (1991), 126–131

[6] Alekseevsky D., Dotti I., Ferraris C., “Homogeneous Ricci positive 5-manifolds”, Pacific J. Math., 175 (1966), 1–12 | MR

[7] Arvanitoyeorgos A., “New invariant Einstein metrics on generalized flag manifolds”, Trans. Amer. Math. Soc., 337:2 (1993), 981–995 | DOI | MR | Zbl

[8] D'Atri J. E., Nickerson H. K., “Geodesic symmetries in spaces with special curvature tensors”, J. Differential Geom., 9 (1974), 251–262 | MR

[9] D'Atri J. E., Ziller W., Naturally reductive metrics and Einstein metrics on compact Lie groups, Mem. Amer. Math. Soc., 18, no. 215, 1979 | MR

[10] Kerr M., “New examples of homogeneous Einstein metrics”, Michigan J. Math., 45 (1998), 115–134 | DOI | MR | Zbl

[11] Kimura M., “Homogeneous Einstein metrics on certain Kähler $C$-spaces”, Adv. Stud. Pure Math., 18:1 (1990), 303–320 | MR | Zbl

[12] Wallach N. R., “Compact homogeneous Riemannian manifolds with strictly positive curvature”, Ann. Math. (2), 96 (1972), 277–295 | DOI | MR | Zbl

[13] Wang M. Y., Ziller W., “Existence and non-existence of homogeneous Einstein metrics”, Invent. Math., 84 (1986), 177–194 | DOI | MR | Zbl