All Questions

Let's start with a definition: Definition: A scalar k-th order differential equation on a smooth manifold $M$, is $F(x,v,\frac{\partial {^\left | \sigma \right |}v}{\partial x^\sigma })=0 $ for $\...

On a smooth n-dimensional Riemannian manifold $M$, suppose I have the kth order partial differential relation (PDR) written in the form: $$\mathcal{R}=\mathcal{R}\left(x^{i},u^{i},u_{j}^{i},u_{jk}^{i}\...

Let $(M, \nabla)$ be a manifold together with a connection on $TM$ and let $T$ be a tensor field on $M$. Suppose the pseudogroup $\Gamma$ of locally defined smooth maps, that simultanously preserve ...