Natural operators lifting functions to cotangent bundles of linear higher order tangent bundles

Mikulski, W. M.. "Natural operators lifting functions to cotangent bundles of linear higher order tangent bundles." Proceedings of the 15th Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1996. [199]-206. <http://eudml.org/doc/220233>.

@inProceedings{Mikulski1996,
abstract = {The author studies the problem how a map $L:M\rightarrow \mathbb \{R\}$ on an $n$-dimensional manifold $M$ can induce canonically a map $A_M(L):T^* T^\{(r)\}M\rightarrow \mathbb \{R\}$ for $r$ a fixed natural number. He proves the following result: “Let $A: T^\{(0,0)\}\rightarrow T^\{(0,0)\}(T^* T^\{(r)\})$ be a natural operator for $n$-manifolds. If $n\ge 3$ then there exists a uniquely determined smooth map $H: \mathbb \{R\}^\{S(r)\}\times \mathbb \{R\}\rightarrow \mathbb \{R\}$ such that $A= A^\{(H)\}$.”The conclusion is that all natural functions on $T^* T^\{(r)\}$ for $n$-manifolds $(n\ge 3)$ are of the form $\lbrace H\circ (\lambda ^\{\langle 0,1\rangle \}_M,\dots , \lambda ^\{\langle r,0\rangle \}_M)\rbrace $, where $H\in C^\infty (\mathbb \{R\}^r)$ is a function of $r$ variables.},
author = {Mikulski, W. M.},
booktitle = {Proceedings of the 15th Winter School "Geometry and Physics"},
keywords = {Proceedings; Geometry; Physics; Winter school; Srni (Czech Republic)},
location = {Palermo},
pages = {[199]-206},
publisher = {Circolo Matematico di Palermo},
title = {Natural operators lifting functions to cotangent bundles of linear higher order tangent bundles},
url = {http://eudml.org/doc/220233},
year = {1996},
}

TY - CLSWK
AU - Mikulski, W. M.
TI - Natural operators lifting functions to cotangent bundles of linear higher order tangent bundles
T2 - Proceedings of the 15th Winter School "Geometry and Physics"
PY - 1996
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [199]
EP - 206
AB - The author studies the problem how a map $L:M\rightarrow \mathbb {R}$ on an $n$-dimensional manifold $M$ can induce canonically a map $A_M(L):T^* T^{(r)}M\rightarrow \mathbb {R}$ for $r$ a fixed natural number. He proves the following result: “Let $A: T^{(0,0)}\rightarrow T^{(0,0)}(T^* T^{(r)})$ be a natural operator for $n$-manifolds. If $n\ge 3$ then there exists a uniquely determined smooth map $H: \mathbb {R}^{S(r)}\times \mathbb {R}\rightarrow \mathbb {R}$ such that $A= A^{(H)}$.”The conclusion is that all natural functions on $T^* T^{(r)}$ for $n$-manifolds $(n\ge 3)$ are of the form $\lbrace H\circ (\lambda ^{\langle 0,1\rangle }_M,\dots , \lambda ^{\langle r,0\rangle }_M)\rbrace $, where $H\in C^\infty (\mathbb {R}^r)$ is a function of $r$ variables.
KW - Proceedings; Geometry; Physics; Winter school; Srni (Czech Republic)
UR - http://eudml.org/doc/220233
ER -