Geodesic
Bundles with multivalued automorphism groups
Matematičeskie zametki, Tome 77 (2005) no. 4, pp. 600-616.

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

A category whose objects are principal bundles with fixed base (smooth manifold) $B$, structure group $T^k$, and finite group $\Delta$ of multivalued automorphisms is constructed; the morphisms are required to be equivariant with respect to $\Delta$. Invariants are found and used to calculate the group of equivalence classes of the category objects. Examples are given and applications to dynamical systems with gyroscopic forces are suggested. 
@article{MZM_2005_77_4_a12,
     author = {A. V. Ryzhkova and E. I. Yakovlev},
     title = {Bundles with multivalued automorphism groups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {600--616},
     publisher = {mathdoc},
     volume = {77},
     number = {4},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_4_a12/}
}
TY  - JOUR
AU  - A. V. Ryzhkova
AU  - E. I. Yakovlev
TI  - Bundles with multivalued automorphism groups
JO  - Matematičeskie zametki
PY  - 2005
SP  - 600
EP  - 616
VL  - 77
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2005_77_4_a12/
LA  - ru
ID  - MZM_2005_77_4_a12
ER  - 
%0 Journal Article
%A A. V. Ryzhkova
%A E. I. Yakovlev
%T Bundles with multivalued automorphism groups
%J Matematičeskie zametki
%D 2005
%P 600-616
%V 77
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2005_77_4_a12/
%G ru
%F MZM_2005_77_4_a12
A. V. Ryzhkova; E. I. Yakovlev. Bundles with multivalued automorphism groups. Matematičeskie zametki, Tome 77 (2005) no. 4, pp. 600-616. http://geodesic.mathdoc.fr/item/MZM_2005_77_4_a12/

[1] Novikov S. P., “Gamiltonov formalizm i mnogoznachnyi analog teorii Morsa”, UMN, 37:5 (1982), 3–49 | MR | Zbl

[2] Yakovlev E. I., “Geodezicheskoe modelirovanie i usloviya razreshimosti dvukhkontsevoi zadachi dlya mnogoznachnykh funktsionalov”, Funktsion. analiz i ego prilozh., 30:1 (1996), 89–92 | MR | Zbl

[3] Yakovlev E. I., “O suschestvovanii reshenii dvukhtochechnykh kraevykh zadach dlya giroskopicheskikh sistem relyativistskogo tipa”, Algebra i analiz, 9:2 (1997), 256–271 | MR

[4] Yakovlev E. I., “Pochti glavnye rassloeniya”, Matem. sb., 190:9 (1999), 151–176 | MR

[5] Bredon G., Vvedenie v teoriyu kompaktnykh grupp preobrazovanii, Nauka, M., 1980 | MR

[6] Khyuzmoller D., Rassloennye prostranstva, Mir, M., 1970

[7] Kobayashi S., “Principal fibre bundles with the $1$-dimensional toroidal group”, Tôhoku Math. J., 8 (1956), 29–45 | DOI | MR

[8] Chzhen Shen-Shen, Kompleksnye mnogoobraziya, IL, M., 1961