On quasijet bundles

Tomáš, Jiří. "On quasijet bundles." Proceedings of the 19th Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2000. 187-196. <http://eudml.org/doc/220810>.

@inProceedings{Tomáš2000,
abstract = {In this paper a Weil approach to quasijets is discussed. For given manifolds $M$ and $N$, a quasijet with source $x\in M$ and target $y\in N$ is a mapping $T^r_xM\rightarrow T^r_yN$ which is a vector homomorphism for each one of the $r$ vector bundle structures of the iterated tangent bundle $T^r$ [A. Dekrét, Casopis Pest. Mat. 111, No. 4, 345-352 (1986; Zbl 0611.58004)]. Let us denote by $QJ^r(M,N)$ the bundle of quasijets from $M$ to $N$; the space $\widetilde\{J\}^r(M,N)$ of non-holonomic $r$-jets from $M$ to $N$ is embeded into $QJ^r(M,N)$. On the other hand, the bundle $QT^r_mN$ of $(m,r)$-quasivelocities of $N$ is defined to be $QJ^r_0(\{\mathbf \{R\}\}^m,N)$; then, $QT^r_m$ is a product preserving functor and so a Weil functor $T^\{\{\mathbf \{Q\}\}^r_m\}$ where $\{\mathbf \{Q\}\}^r_m$ is the Weil algebra $QT^r_m\{\mathbf \{R\}\}$ [see I. Kolár, P. Michor and J. Slovák, ‘Natural operations in differential geometry’ (Springer-Verlag, Berlin) (1993; Zbl 0782.53013)]; next, t!},
author = {Tomáš, Jiří},
booktitle = {Proceedings of the 19th Winter School "Geometry and Physics"},
keywords = {Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)},
location = {Palermo},
pages = {187-196},
publisher = {Circolo Matematico di Palermo},
title = {On quasijet bundles},
url = {http://eudml.org/doc/220810},
year = {2000},
}

TY - CLSWK
AU - Tomáš, Jiří
TI - On quasijet bundles
T2 - Proceedings of the 19th Winter School "Geometry and Physics"
PY - 2000
CY - Palermo
PB - Circolo Matematico di Palermo
SP - 187
EP - 196
AB - In this paper a Weil approach to quasijets is discussed. For given manifolds $M$ and $N$, a quasijet with source $x\in M$ and target $y\in N$ is a mapping $T^r_xM\rightarrow T^r_yN$ which is a vector homomorphism for each one of the $r$ vector bundle structures of the iterated tangent bundle $T^r$ [A. Dekrét, Casopis Pest. Mat. 111, No. 4, 345-352 (1986; Zbl 0611.58004)]. Let us denote by $QJ^r(M,N)$ the bundle of quasijets from $M$ to $N$; the space $\widetilde{J}^r(M,N)$ of non-holonomic $r$-jets from $M$ to $N$ is embeded into $QJ^r(M,N)$. On the other hand, the bundle $QT^r_mN$ of $(m,r)$-quasivelocities of $N$ is defined to be $QJ^r_0({\mathbf {R}}^m,N)$; then, $QT^r_m$ is a product preserving functor and so a Weil functor $T^{{\mathbf {Q}}^r_m}$ where ${\mathbf {Q}}^r_m$ is the Weil algebra $QT^r_m{\mathbf {R}}$ [see I. Kolár, P. Michor and J. Slovák, ‘Natural operations in differential geometry’ (Springer-Verlag, Berlin) (1993; Zbl 0782.53013)]; next, t!
KW - Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)
UR - http://eudml.org/doc/220810
ER -