Geodesic
Rescaling of the metric, invariant operators, and spontaneous compactification
Teoretičeskaâ i matematičeskaâ fizika, Tome 77 (1988) no. 1, pp. 88-96 
D. V. Vassilevich; V. D. Lyakhovsky; N. N. Shtykov. Rescaling of the metric, invariant operators, and spontaneous compactification. Teoretičeskaâ i matematičeskaâ fizika, Tome 77 (1988) no. 1, pp. 88-96. http://geodesic.mathdoc.fr/item/TMF_1988_77_1_a7/
@article{TMF_1988_77_1_a7,
     author = {D. V. Vassilevich and V. D. Lyakhovsky and N. N. Shtykov},
     title = {Rescaling of the metric, invariant operators, and spontaneous compactification},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {88--96},
     year = {1988},
     volume = {77},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_77_1_a7/}
}
TY  - JOUR
AU  - D. V. Vassilevich
AU  - V. D. Lyakhovsky
AU  - N. N. Shtykov
TI  - Rescaling of the metric, invariant operators, and spontaneous compactification
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1988
SP  - 88
EP  - 96
VL  - 77
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1988_77_1_a7/
LA  - ru
ID  - TMF_1988_77_1_a7
ER  - 
%0 Journal Article
%A D. V. Vassilevich
%A V. D. Lyakhovsky
%A N. N. Shtykov
%T Rescaling of the metric, invariant operators, and spontaneous compactification
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1988
%P 88-96
%V 77
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1988_77_1_a7/
%G ru
%F TMF_1988_77_1_a7

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

A criterion for enlargement of the symmetry of a $G$-invariant metric on $G/H$ to the symmetry of a $G'$-invariant metric on $G'/H'$ is formulated and proved. The complete set of vacuum solutions of $d=11$ supergravity on $S^7$ and the spectrum of the Laplace–Beltrami operator for each of the solutions are obtained. The degeneracy of the spectrum of the invariant operators resulting from rescaling with symmetry enlargement is investigated.

[1] Castellani L., Romans L. J., Warner N. P., Ann. Phys., 157:2 (1984), 394–408 | DOI | MR

[2] Duff M. J., Nilsson B. E. W., Pope C. N., Nucl. Phys., B233:3 (1984), 433–456 | DOI | MR | Zbl

[3] Vasilevich D. V., YaF, 45:1 (1987), 282–286 | MR

[4] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, T. 2, Nauka, M., 1981 | MR

[5] Vasilevich D. V., Lyakhovskii V. D., TMF, 66:3 (1986), 350–359 | MR | Zbl

[6] Awada M. A., Duff M. J., Pope C. N., Phys. Rev. Lett., 50:5 (1983), 294–297 | DOI | MR

[7] Pope C. N., Warner N. P., Phys. Lett., 150B:5 (1985), 352–356 | DOI | MR

[8] Slansky R., Phys. Rep., 79:1 (1981), 1–128 | DOI | MR

[9] Duff M. J., Nilsson B. E. W., Pope C. N., Phys. Rev. Lett., 50:26 (1983), 2043–2047 | DOI | MR

[10] Page D. N., Phys. Rev., D28:12 (1985), 2976–2982 | MR

[11] Duff M. J., Nilsson B. E. W., Pope C. N., Phys. Rep., 130:1 (1986), 1–142 | DOI | MR

[12] Coquereaux R., Jadczyk A., Commun. Math. Phys., 98:1 (1985), 79–104 ; Glass. Quant. Grav., 3:1 (1986), 29–42 ; Consistency of the $G$-invariant Kaluza–Klein scheme, Preprint TH. 4305/85, CERN, Geneva, 1985 | DOI | MR | Zbl | DOI | MR | Zbl