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Results tagged with jets
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user 13972
7
votes
A linear representation of the group of jets at 0 under composition
I think you want to look at Faà di Bruno's formula, and the description of composition of formal power series, particularly the historical remarks.
The linear representation of this group that allows …
- 108k
6
votes
Accepted
The bundle of symmetric affine connections as quotient of the second-order frame bundle
the space of torsion-free affine connections is identified with the space of sections of the $\mathrm{GL}_n(\mathbb{R})$-quotient of the submanifold $J^1_0(F^*(M))\subset J^1(F^*(M))$ consisting of $1$-jets …
- 108k
14
votes
Accepted
A variant of the Monge-Cayley-Salmon theorem?
Setting aside the assumption that $\phi$ be a polynomial mapping for the moment (however, see below for a construction of a large family of polynomial solutions), if one makes the 'nondegeneracy' assu …
- 108k
9
votes
Accepted
Induced Riemannian metric on Jet-Manifold
There are, of course, several different functorially induced metrics on $J^r(M,N)$ when $M$ and $N$ are endowed with given Riemannian metrics.
For example, $J^0(M,N)=M\times N$ and one can just tak …
- 108k