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Start Over Subject classical linear connection

1. Higher order jet involution

Creator:
Doupovec, Miroslav and Mikulski, Włodzimierz M.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
jet prolongation, classical linear connection, and higher order connection
Language:
English
Description:
We introduce an exchange natural isomorphism between iterated higher order jet functors depending on a classical linear connection on the base manifold. As an application we study the prolongation of higher order connections to jet bundles.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. The natural operators lifting connections to higher order cotangent bundles

Creator:
Mikulski, Włodzimierz M.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
classical linear connection and natural operator
Language:
English
Description:
We prove that the problem of finding all ${\mathcal {M} f_m}$-natural operators ${C\colon Q\rightsquigarrow QT^{r*}}$ lifting classical linear connections $\nabla $ on $m$-manifolds $M$ into classical linear connections $C_M(\nabla )$ on the $r$-th order cotangent bundle $T^{r*}M=J^r(M,\mathbb R )_0$ of $M$ can be reduced to the well known one of describing all $\mathcal {M} f_m$-natural operators $D\colon Q\rightsquigarrow \bigotimes ^pT\otimes \bigotimes ^qT^*$ sending classical linear connections $\nabla $ on $m$-manifolds $M$ into tensor fields $D_M(\nabla )$ of type $(p,q)$ on $M$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public