Vessiot distribution

[Tehseen 2014]

For finite $k$, Cartan distribution $\mathcal{C}$ is generated by

$$ D_{x^i}^{(k)} :=\partial x_{i}+\sum_{\alpha=1}^{q} \sum_{0 \leq|J|Cartan distribution restricted to the submanifold $\mathcal{S}$ of $J^k(E)$ given by a system of DEs is known as the Vessiot distribution. See also [Vitagliano 2017] page 22, where it defines the distribution:

$$ \mathcal{C}(\mathcal{S}):z\mapsto \mathcal{C}(\mathcal{S})_z:=\mathcal{C}_z \cap T_z \mathcal{S} $$

In general, is not Frobenius integrable, but Vessiot gave a method to construct all the integrable subdistributions for a given distribution.

The integral manifolds of this distribution are the solutions of system of DEs (provided they have the proper dimension, I guess...)

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Author of the notes: Antonio J. Pan-Collantes

antonio.pan@uca.es

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