Given a $n$-manifold $M$ we can consider for every $0
We will denote the points of $G(r,TM)$ as pairs $(p,E)$ with $p\in M$ and $E\in G(r,T_p M)$.
The space $G(r,TM)$ carries a canonical linear Pfaffian system: the one whose integral manifolds are exactly the lifts to $G(r,TM)$ of mappings
$$ f:N^r \to M $$where the lift is defined by $\tilde{f}(x)=(f(x),T_{f(x)} f(N))$.
It can also be defined by
$$ I_{(p,E)}:=\pi^*(E^{\perp}) $$ $$ J_{(p,E)}:=\pi^*(T^*_p M) $$________________________________________
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Author of the notes: Antonio J. Pan-Collantes
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