Geodesic
Tangent and tensor bundles of $(2,0)$ type under Lie group
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Труды геометрического семинара, Tome 147 (2005) no. 1, pp. 138-147 
N. A. Opokina. Tangent and tensor bundles of $(2,0)$ type under Lie group. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Труды геометрического семинара, Tome 147 (2005) no. 1, pp. 138-147. http://geodesic.mathdoc.fr/item/UZKU_2005_147_1_a12/
@article{UZKU_2005_147_1_a12,
     author = {N. A. Opokina},
     title = {Tangent and tensor bundles of $(2,0)$ type under {Lie} group},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {138--147},
     year = {2005},
     volume = {147},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2005_147_1_a12/}
}
TY  - JOUR
AU  - N. A. Opokina
TI  - Tangent and tensor bundles of $(2,0)$ type under Lie group
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2005
SP  - 138
EP  - 147
VL  - 147
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/UZKU_2005_147_1_a12/
LA  - ru
ID  - UZKU_2005_147_1_a12
ER  - 
%0 Journal Article
%A N. A. Opokina
%T Tangent and tensor bundles of $(2,0)$ type under Lie group
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2005
%P 138-147
%V 147
%N 1
%U http://geodesic.mathdoc.fr/item/UZKU_2005_147_1_a12/
%G ru
%F UZKU_2005_147_1_a12

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In the E. V. Nazarova's work the tangent bundle of $TG$ Lie group was studied from the natural and synectics extension point of view of this group in algebra of dual numbers. Invariant synectics linkages under group $G$. Our aim was to study the tangent and tensor bundles $T^2_0G$ under Lie group. These bundles were proved to be trivial and the bundle spaces were proved to be Lie groups. The lifts of these left-invariant vector fields were built un these bundles. Lie algebra of $TG$ group and Lie algebra of $T^2_0G$ under Lie group were found, and the equations of these algebras were obtained. The tangent and $(2,0)$ tensor bundles under 2-dimensional linked Lie groups were regarded as examples.

[1] Vinberg E. B., Gorbatsevich V. V., Onischik A. L., Stroenie grupp i algebr Li, Itogi nauki i tekhn. VINITI. Sovr. probl. matem., 41, 1990, 254 pp. | MR | Zbl

[2] Gavrilov S. P., “Geodezicheskie levoinvariantnykh metrik na svyaznoi dvumernoi neabelevoi gruppe Li”, Gravitatsiya i teoriya otnositelnosti, Izd-vo Kazan. un-ta, Kazan, 1981, 28–44 | MR

[3] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, v. 1, Nauka, M., 1987, 344 pp. | MR

[4] Mischenko A. S., Vektornye rassloeniya i ikh primeneniya, Nauka, M., 1984, 208 pp. | MR

[5] Nazarova E. V., “K geometrii kasatelnykh rassloenii grupp Li”, Tr. geom. sem., Izd-vo Kazan. un-ta, Kazan, 1979, 70–78 | MR

[6] Postnikov M. M., Lektsii po geometrii. Semestr 5. Differentsialnaya geometriya, Nauka, M., 1979, 312 pp. | MR

[7] Khyuzmoller D., Rassloennye prostranstva, Mir, M., 1979, 442 pp.

[8] Shapukov B. N., Zadachi po gruppam Li i ikh prilozheniyam, NITs “RKhD”, M., 2002, 256 pp.

[9] Shapukov B. N., “Tenzornye rassloeniya”, Pamyati Lobachevskogo posvyaschaetsya, Izd-vo Kazan. un-ta, Kazan, 1992, 104–125 | MR