Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Труды геометрического семинара, Tome 147 (2005) no. 1, pp. 148-153
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V. I. Panzhenskij. On infinitesimal automorphisms of almost symplectic structures. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Труды геометрического семинара, Tome 147 (2005) no. 1, pp. 148-153. http://geodesic.mathdoc.fr/item/UZKU_2005_147_1_a13/
@article{UZKU_2005_147_1_a13,
author = {V. I. Panzhenskij},
title = {On infinitesimal automorphisms of almost symplectic structures},
journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
pages = {148--153},
year = {2005},
volume = {147},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZKU_2005_147_1_a13/}
}
TY - JOUR
AU - V. I. Panzhenskij
TI - On infinitesimal automorphisms of almost symplectic structures
JO - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY - 2005
SP - 148
EP - 153
VL - 147
IS - 1
UR - http://geodesic.mathdoc.fr/item/UZKU_2005_147_1_a13/
LA - ru
ID - UZKU_2005_147_1_a13
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%0 Journal Article
%A V. I. Panzhenskij
%T On infinitesimal automorphisms of almost symplectic structures
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2005
%P 148-153
%V 147
%N 1
%U http://geodesic.mathdoc.fr/item/UZKU_2005_147_1_a13/
%G ru
%F UZKU_2005_147_1_a13
On the tangent bundle $TM$ of a manifold $M$ endowed with an almost symplectic structure $\omega$ and a linear connection $\nabla$ compatible with $\omega$, we consider the Riemannian metric $G$ which is Hermitian with respect to the canonical almost complex structure $J$ and the corresponding almost symplectic structure $\Omega$. We study the infinitesimal automorphisms of these structures on $TM$, and, in particular, prove that the dimension of the Lie algebra of natural automorphisms of $G$ and of $\Omega$ is less than or equal to $n(n+3)/2$.
