Complete separation of variables in the free Hamilton–Jacobi equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 2, pp. 250-269
V. G. Bagrov; V. V. Obukhov. Complete separation of variables in the free Hamilton–Jacobi equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 2, pp. 250-269. http://geodesic.mathdoc.fr/item/TMF_1993_97_2_a7/
@article{TMF_1993_97_2_a7,
     author = {V. G. Bagrov and V. V. Obukhov},
     title = {Complete separation of variables in the free {Hamilton{\textendash}Jacobi} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {250--269},
     year = {1993},
     volume = {97},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_97_2_a7/}
}
TY  - JOUR
AU  - V. G. Bagrov
AU  - V. V. Obukhov
TI  - Complete separation of variables in the free Hamilton–Jacobi equation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1993
SP  - 250
EP  - 269
VL  - 97
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1993_97_2_a7/
LA  - ru
ID  - TMF_1993_97_2_a7
ER  - 
%0 Journal Article
%A V. G. Bagrov
%A V. V. Obukhov
%T Complete separation of variables in the free Hamilton–Jacobi equation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1993
%P 250-269
%V 97
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1993_97_2_a7/
%G ru
%F TMF_1993_97_2_a7

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

The theory of Stäckel spaces is generalized to the case when the coordinate system in which there is complete separation of variables in the free Hamilton–Jacobi equation contains complex variables. Theorems which establish necessary and sufficient criteria of such spaces are proved.

[1] Stackel P., Compt. Rend. Hebd. Acad. Sci., 116 (1893), 1284–1286; 485–487 | Zbl

[2] Shapovalov V. N., O privedenii k kanonicheskomu vidu veschestvennykh kvadratichnykh form, deponirovano v VINITI 2780-75

[3] Shapovalov V. N., Izv. vuzov. Fizika, 1978, no. 9, 17–27 | MR

[4] Shapovalov V. N., Sib. mat. zhurnal, XX:5 (1979), 1117–1130 | MR | Zbl

[5] Shapovalov V. N., Dif. uravneniya, XVI:10 (1980), 1863–1874 | MR

[6] Eisenhart L. P., Proc. Nat. Acad. Sci., 35 (1949), 412–418 | DOI | MR | Zbl

[7] Smorodinskii Ya. A., Tugov I. I., ZhETF, 50:3 (1966), 653–658 | MR

[8] Shapovalov V. N., Izv. vuzov. Fizika, 1975, no. 6, 57–63

[9] Shapovalov V. N., Ekle G. G., Algebraicheskie svoistva uravnenii Diraka, KGU, Elista, 1972

[10] Bagrov V. G., Shapovalov A. V., Evseevich A. A., Preprint No 9 Tomskogo filiala SO AN SSSR, 1988

[11] Bagrov V. G., Obukhov V. V., Preprint No 10 Tomskogo filiala SO AN SSSR, 1988 ; No 11, 1988; No 22, 1990 | MR

[12] Chernikov N. A., Shavokhina N. S., TMF, 14:3 (1973), 310–317

[13] Bagrov V. G., Obukhov V. V., Izv. vuzov. Fizika, 1988, no. 9, 25–27 | MR

[14] Obukhov V. V., Razdelenie peremennykh v skalyarnykh i spinornykh uravneniyakh v OTO, Dokt. diss., OIYaI, Dubna, 1990

[15] Eizenkhart L. P., Nepreryvnye gruppy preobrazovanii, IL, M., 1947, 61–63

[16] Eizenkhart L. P., Rimanova geometriya, IL, M., 1948

[17] Gantmakher F. P., Teoriya matrits, TTL, M., 1953, 167 | MR

[18] Veblen O., Proc. Nat. Acad. Sci. USA, no. 8, 74