Holomorphic Tensor Fields and Linear Connections on a Second Order Tangent Bundle
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 36-50
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The second order tangent bundle $T^2M$ of a smooth manifold $M$ carries a natural structure of a smooth manifold over the algebra $\mathbf R(\varepsilon^2)$ of truncated polynomials of degree 2. A section $\sigma$ of $T^2M$ induces an $\mathbf R(\varepsilon^2)$-smooth diffeomorphism $\Sigma\colon T^2M\to T^2M$. Conditions are obtained under which an $\mathbf R(\varepsilon^2)$-smooth tensor field and an $\mathbf R(\varepsilon^2)$-smooth linear connection on $T^2M$ can be transfered by a diffeomorphism of the form $\Sigma$, respectively, into the lift of a tensor field and the lift of a linear connection given on $M$.
Keywords:
tangent bundle of second order, lift of a linear connection, lift of a tensor field, holomorphic connection, Lie derivative.
@article{UZKU_2009_151_4_a3,
author = {F. R. Gainullin and V. V. Shurygin},
title = {Holomorphic {Tensor} {Fields} and {Linear} {Connections} on {a~Second} {Order} {Tangent} {Bundle}},
journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
pages = {36--50},
publisher = {mathdoc},
volume = {151},
number = {4},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a3/}
}
TY - JOUR AU - F. R. Gainullin AU - V. V. Shurygin TI - Holomorphic Tensor Fields and Linear Connections on a Second Order Tangent Bundle JO - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki PY - 2009 SP - 36 EP - 50 VL - 151 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a3/ LA - ru ID - UZKU_2009_151_4_a3 ER -
%0 Journal Article %A F. R. Gainullin %A V. V. Shurygin %T Holomorphic Tensor Fields and Linear Connections on a Second Order Tangent Bundle %J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki %D 2009 %P 36-50 %V 151 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a3/ %G ru %F UZKU_2009_151_4_a3
F. R. Gainullin; V. V. Shurygin. Holomorphic Tensor Fields and Linear Connections on a Second Order Tangent Bundle. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 36-50. http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a3/