Vessiot distribution

[Tehseen 2014]

For finite $k$ , Cartan distribution $C$ is generated by

$$ D_{x^i}^{(k)} :=\partial x_{i}+\sum_{\alpha=1}^{q} \sum_{0 \leq|J|Cartan distribution restricted to the submanifold

S

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:

C (S) : z \mapsto C (S)_{z} := C_{z} \cap T_{z} 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

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